The Pennsylvania State University The Graduate School College of Engineering NONLINEAR ACTIVE VIBRATION BASED DAMAGE DETECTION AND LOCALIZATION

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1 The Pennsylvania State University The Graduate School College of Engineering NONLINEAR ACTIVE VIBRATION BASED DAMAGE DETECTION AND LOCALIZATION A Thesis in Aerospace Engineering by Justin A. Long 214 Justin A. Long Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 214

2 The thesis of Justin A. Long was reviewed and approved by the following: Stephen C. Conlon Associate Professor of Aerospace Engineering Senior Research Associate PSU Applied Research Laboratory Thesis Advisor Edward C. Smith Professor of Aerospace Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering Signatures are on file in the Graduate School. ii

3 Abstract The development of damage detection, localization, and automation procedures is critical for a practical implementation of Structural Health Monitoring (SHM) in airframe structures. Effective SHM can assure the safety and reliability of aircraft, while reducing costly maintenance time associated with traditional visual inspections. In this thesis a nonlinear spectroscopy-based detection and localization approach was developed on a stiffened aluminum plate test bed, representative of typical skinstiffener joints on airframe structures. Damage conditions were induced to represent working rivets and loss of torque in fasteners, common precursors to fatigue crack propagation. Active vibration sources were used to excite the structure, and strain sensor rosettes were used to measure the nonlinear vibration responses from the damage. Estimates of the damage location were obtained by using a Principal Strain based Localization (PSL) approach, to estimate the direction of wave propagation associated with the nonlinear signature from the damage location. An emphasis was placed on the use of minimal sensors and actuators, for a lightweight and practical implementation on aircraft. A systematic approach was developed for evaluating the PSL estimates using acquired strain time records. Strain amplitudes were processed at the nonlinear frequency components, and potential automation methods were developed. Optimal drive frequency selections were made by a direct comparison of damaged structure nonlinear responses with a healthy baseline. The drive condition corresponding to the highest increase in nonlinear response was studied, at various active drive levels, to determine effective forcing required for accurate localization using the PSL technique. The undamped stiffened plate configuration was used for development of both single tone and modulated wave nonlinear damage detection methods. Single tone transient methods were explored, but the technique was hampered by low signal-tonoise at the nonlinear components. A steady-state single tone excitation resulted in higher signal-to-noise estimates, but results were degraded by reverberation effects from the plate boundaries. Using the modulated wave approach with a constant exercising wave (low drive) frequency of 75 Hz, high sensitivity detection (up to iii

4 15 db) was achieved in both 3 rows loose and 1 row loose damage conditions, with probing wave (high drive) frequencies of 6 Hz and 5 Hz, respectively. Accurate localization results were obtained with the use of low force levels, on the order of 1 N in amplitude. PSL angle estimates showed a weak dependence on reverberation radius estimates for the plate, but showed a strong dependence on forcing amplitude. Angle estimates were most accurate at low drive levels, where the strain response showed discrete sideband amplitudes. At higher force amplitudes, angle estimates were degraded, due to apparent nonlinear damping effects, and the development of a broadband chaotic response. In the edge-damped plate configuration, localization results were enhanced in the steady-state single tone approach, due to increased absorption at the plate boundaries. However, the broadband chaotic response degraded estimates at higher force levels. The modulated wave approach showed 1-2 db detection sensitivity in the tested damage conditions. In addition, a low nonlinear response was shown in the healthy condition. This was due to the decrease in nonlinearity from the plate boundaries, a result of the added edge damping treatment. Compared to the undamped plate configuration, adjustments in probing wave drive frequency and forcing were necessary to induce sufficient nonlinear response. Many of the optimal drive frequencies were observed to be near the critical frequency of the plate (48 Hz), where acoustic radiation damping losses are largest. However, required force levels were considered low enough for the use of low power, lightweight actuators in both damped and undamped plate test beds (<1 N of force amplitude across all test cases). The modulated wave PSL method was successfully transitioned for use in airframe structures. An excitation corresponding to the blade passage of the UH-6 was used as a low frequency source on the stiffened plate, an approach that would reduce the weight and power requirements in an embedded application. An active drive approach was used on a laboratory UH-6 upper cabin test bed with simulated damage, showing up to 2 db in detection sensitivity. The developed experimental approaches represent a key step in the use of nonlinear vibration based methods, in particular wave modulation, for embedded airframe SHM applications. iv

5 Table of Contents List of Figures List of Tables Acknowledgments viii xix xx Chapter 1 Introduction Background Structural Health Monitoring Application to Airframe Structures Linear Vibration and Guided Wave Methods Nonlinear Vibration Based Damage Detection Overview Theoretical Development Higher Harmonics and Wave Modulation Subharmonics, Ultra-Subharmonics, Ultra-Frequency Pairs, and Chaotic Response NDE Applications Penn State Airframe SHM Applications Damage Localization Objectives and Outline Research Objectives Thesis Outline Chapter 2 Experimental Setup and Methods Development Stiffened Plate Test Bed Single Tone Data Processing Techniques Initial Acoustic Source Testing v

6 2.4 Modulated Wave Data Processing and Automation Techniques Damping Effects Reverberation Radius Damped Stiffened Plate Loss Factor Measurements Nonlinear Regime Measurements Method Summary and Approach Chapter 3 Undamped Stiffened Plate Results Single-tone Damage Detection Results Steady-state Localization Results Transient Localization Results Modulated Wave Damage Detection Results Rows Loose Damage Condition Row Loose Damage Condition Summary of Undamped Plate Results Chapter 4 Damped Stiffened Plate Results Single Tone Damage Detection Results Modulated Wave Damage Detection Results Rows Loose Damage Condition Row Loose Damage Conditions Summary of Damped Plate Results Chapter 5 Airframe Applications Rotor Blade Passage as a Low Frequency Source UH-6 Upper Cabin Testing Experimental Setup and Procedure Loose Fastener Damage Conditions Chapter 6 Conclusions Summary of Key Results Data Processing and Automation Undamped Stiffened Plate Results Damping Effects vi

7 6.1.4 Airframe Results and Applications Future Work Appendix A Extra Data Sets 119 A.1 Acoustic Source Vector Plots A.2 Undamped Plate Transient Localization Time Records A.3 Damped Plate Transient Localization Time Records A.4 Damped Plate Modulated Wave Results A Rows Loose Damage Localization A.4.2 Mid-Plate 1 Row Loose Damage Localization A.4.3 Upper-Plate 1 Row Loose Damage Localization A.5 Airframe Results A Loose Damage Condition A Loose Damage Condition Appendix B Principal Strain Localization 145 B.1 Processing Steps B.2 Processing Code Bibliography 161 vii

8 List of Figures 1.1 Fatigue damage initiation sites, documented by (a) AugustaWestland [1] and (b) Campbell and Lahey [8] UH-6A Black Hawk upper cabin and OH-58D Kiowa Warrior tailboom, with common fatigue damage initiation sites highlighted. An embedded SHM system could detect damage at these hot spots in realtime, alleviating the costly downtime associated with visual inspections Traditional guided wave approach. A tone burst signal is sent by a source and received by various sensors on the structure. A scattered signal shows the presence of damage, and damage can be localized using the associated time of flight of the scattered waveform. In general, a complex network of actuators and sensors is required for accurate detection and localization SMART Layer sensor installed on an OH-58D tailboom in order to monitor the golden rivet region of the structure. The layer contains 8 piezoelectric sensor/actuators (figure from Ref. [18]) Example healthy strain amplitude in the presence of a single tone excitation (A), damaged response exhibiting higher harmonics, subharmonics, and ultra-subharmonics of the drive frequency (B), healthy response in the presence of two interrogation frequencies (C), and damaged response showing multiple plus and minus sidebands centered around the high drive frequency (D) Nonlinear regimes associated with the coupled nonlinear oscillator model of a damaged material response, where the nature of the nonlinear response is dependent on the drive amplitude and drive frequency ν (figure from [37]) Damage detection results using both nonlinear strain and NSSI metrics on the stiffened aluminum plate test bed [46]. Results show the detection benefits of the NSSI approach. Localization of damage was not addressed in previous studies viii

9 1.8 NSSI sensor suite featuring 3 piezoelectric strain sensors in a rectangular rosette configuration and 2 uni-axial accelerometers. The inherent data fusion of NSSI results in a high sensitivity detection metric Comparison of rectangular and delta strain rosette configurations. These are the two most common rosettes used in measurements of strain for principal axis calculations Physical representation of the damage as a virtual source in the system. Energy from the two collocated active drive frequencies is scattered into nonlinear components. Strain measurements of the nonlinear amplitudes provide information about the direction of the incoming damage induced signatures Stiffened aluminum plate test bed (775 aluminum alloy, 89 cm x 58 cm x.25 cm), instrumented with 3 piezoelectric strain sensor rosettes (PCB Piezotronics 74B2). A collocated low/high frequency shaker assembly (Wilcoxon F4/F7) provided two active drive sources. A damaged joint condition was induced by loosening rows of fasteners along the joint Flowchart of data acquisition, sensor and actuator hardware used throughout this study Principal strain localization processing algorithm for both transient (red) and steady state (blue) single tone excitations. Note that repeated estimates may be calculated from multiple rosettes, frequency components, and additional averaging Acoustic source localization testing setup. The high frequency F7 shaker was mounted directly to the unstiffened plate, at various bolt hole positions. A progression of PSL localization tests was performed using steady-state and transient signals Strain amplitude spectra for each gage in Rosette 1, using a steadystate excitation of 2 khz at the center position on the plate. These strain amplitudes were extracted and used to localize the source using the PSL processing method outlined in Section Strain measurements for each gage in Rosette 1, using a tone burst excitation of 2 khz at the center position on the plate. The time signal was filtered and enveloped. Strain amplitudes were chosen from the first group arrival in the enveloped waveform PSL position estimates for various source positions (shown in green) on the aluminum plate. A 2 Hz drive frequency was used, with a bending wavelength of 11.1 cm. This resulted in approximately 2 4 propagation wavelengths between the source and receivers ix

10 2.8 Principal strain localization algorithm for a steady-state modulated wave excitation. Nonlinear sideband amplitudes are extracted, lowlevel sidebands (<1 db signal-to-noise in this study) are sifted out of the routine, and high signal-to-noise components are summed for each sensor in a rosette. These total nonlinear contributions are then run through the PSL routine to estimate the damage location Proposed algorithm for nonlinear modulated wave localization and automation. A direct comparison between healthy and damaged conditions is used to select drive frequencies. Further processes are used to evaluate drive levels necessary for accurate localization. This process was carried out systematically for different test beds and damage conditions Soundcoat 66 edge damping treatment (1.5 cm wide x 1.3 mm thick) used on the stiffened aluminum plate test bed Healthy OTO band loss factor measurements on the stiffened aluminum panel from 1 khz to 2 khz. Edge damping treatment is shown to increase loss factors in all frequency bands Damaged (3 fastener rows loose) OTO band loss factor measurements on the stiffened aluminum panel. Loss factors are shown to increase in the bands above 63 Hz Damping increase factors for both healthy and damaged conditions on the stiffened aluminum panel. Damping is shown to increase at each center frequency in the healthy condition, while the damaged condition shows both increased and decreased damping in the frequencies below 63 Hz. This could be due to nonlinear damping effects from the damaged joint condition Wavelengths for bending, longitudinal, and shear waves traveling in a.25 cm thickness aluminum plate, similar to the stiffened aluminum plate test bed. The critical frequency of the plate is shown at 48 Hz Calculated reverberation radius for the damaged plate condition, in both damped and undamped plate configurations. The largest reverberation distance corresponds to the point of highest structural damping Sketch of approximate reverberation radius (in red) for the 3 rows loose damage condition. Typical distances from the damage to each sensor rosette are shown. Throughout localization testing, all sensors were mounted at distances greater than the maximum reverberation radius of 7 cm x

11 2.17 Strain response showing a progression from orderly higher harmonic content to unstable subharmonic and ultra-subharmonic response. Low levels of nonlinearity are shown in the healthy response Strain response at higher drive levels, exhibiting growth of the broadband chaotic response. The healthy condition begins to show signs of ultra-frequency pairs around the drive frequency and higher harmonics Narrowband view of 22 Hz drive in.43 N and 1.1 N forcing conditions. The damaged response shows ultra-frequency pair content at lower force amplitudes. The healthy condition also shows ultrafrequency pairs, but at higher forcing levels where the damaged condition has already transitioned to chaos Largest damage increment, with 3 fastener rows loose. This created approximately a 15 cm x 2.5 cm gap in the plate/stiffener interface Damaged versus healthy strain responses for rosette 1, under a single tone excitation at 2227 Hz, -8 db. The damaged response shows high subharmonic and ultra-subharmonic responses, as well as ultrafrequency pairs around the drive frequency and higher harmonics Single tone, steady-state damage localization estimates performed using each nonlinear component individually, as well as a total nonlinear estimate. The source position is shown in green, while the damage size and location is shown in red Transient tone burst force signal at 2227 Hz, with amplitude of 1.5 N. After the initial 5-cycle pulse, reflections from the boundaries appear in the impedance head response Transient response for rosette 3, filtered at the f/2 subharmonic. The first group arrival of the nonlinear component is near the.5 s. Gage 2 shows a peak amplitude of.25 µ-s Transient PSL angle estimates, focusing on nonlinear subharmonics and ultra-subharmonics of 2227 Hz. The f/2 estimate is comparable to that in the steady-state case Tested damage conditions on the undamped stiffened plate, using a modulated wave excitation. In addition to the 3 rows loose damage size, a 1 row loose condition was assessed Damaged versus healthy sideband amplitude ratios for the 3 rows loose damage condition, in the undamped plate configuration. A peak condition is shown at 6 khz, where the 4f sideband component (gage 2) shows a 15 db increase from healthy to damaged conditions. This drive frequency was chosen for further examination xi

12 3.9 Damaged versus healthy strain spectra for each gage in rosette 1, using a 6 khz high frequency drive. The minus sideband components show high sensitivity to the damage condition High frequency amplitude sensitivity for the modulated wave angle estimates, in the 3 rows loose, undamped configuration. The most accurate angle result is shown at a high frequency drive amplitude of -3.2 db Amplitude spectrum of strain rosette 3, gage 1, showing an increase in nonlinear component amplitudes with increasing drive amplitude. A resulting increase in reverberation effects could lead to degradation of the PSL estimate Low frequency amplitude sensitivity for the modulated wave angle estimates, in the 3 rows loose, undamped configuration. The most accurate result is shown at a low frequency drive amplitude of -7.3 db. Past this drive level, nonlinear effects at the boundaries of the structure, as well as nonlinear damping effects, may cause the PSL estimates to degrade Repeatability study for the modulated wave angle estimates, in the 3 rows loose, undamped configuration. Steady-state drives consisted of 6 Hz (-3.2 db force amplitude) and 75 Hz (-7.3 db force amplitude) Repeatable damage localization result for the 3 rows loose, undamped plate configuration. The drive source is shown in green, the vectors from the rosette positions are shown in blue, and the damage location is outlined in red. In an airframe application, this result would allow maintenance crews to easily detect and repair damage without the lengthy downtime associated with visual inspections Damaged versus healthy sideband amplitude ratios for the 1 row loose damage condition, in the undamped plate configuration. A peak condition is shown at 5 khz, where the f2 sideband component shows >1 db increase in both gages 1 and Damaged versus healthy strain spectra for each gage in rosette 1, using the 5 khz high frequency drive. The f2 sideband components show a >1 db increase in the damaged condition High frequency amplitude sensitivity for the modulated wave angle estimate, in the 1 row loose, undamped configuration. Accurate angle estimates are shown up to the drive condition where a broadband chaotic response takes place xii

13 3.18 Amplitude spectrum of strain rosette 2, gage 2, showing a transition to a broadband chaotic state at the -4.4 db force level. This has a negative impact on PSL angle estimates when attempting to localize on the damage Low frequency amplitude sensitivity in the 1 row loose, undamped plate configuration. The most accurate result is shown at a drive amplitude of.5 db Repeatability study for the 1 row loose, undamped plate configuration. Steady-state drives consisted of 5 Hz (-6 db force amplitude) and 75 Hz (.5 db force amplitude) Repeatable damage localization result for the 1 row loose, undamped plate configuration. The PSL estimate accurately detects the small damage size (5 cm x 2.5 cm) Subharmonic and ultra-subharmonic amplitudes under increasing force amplitude, with an active drive frequency of 22 Hz in the damped plate configuration. The trend shows a gradual decrease in nonlinear response at the discrete subharmonic and ultra-subharmonic frequencies, once the chaotic response begins at -3.7 db Rosette 3, gage 3 strain amplitude spectrum for the 22 Hz single tone excitation, at the -3.7 db drive level. At this point, the nonlinear signatures show the highest signal-to-noise, and therefore damage localization estimates are most accurate. Past this drive level, the broadband chaotic response dominates Drive amplitude sensitivity study for the single tone interrogation at 22 Hz, in the 3 row loose, damped plate configuration. Accurate angle estimates are shown for all rosettes, though slight degradation is observed where the broadband chaotic response takes place, past -3.7 db. This effect is minimal for rosettes 1 and 2, but more prominent for rosette Total nonlinear PSL estimate for the single tone -3.7 db forcing condition, in the damped plate configuration All tested damage conditions on the damped stiffened plate, using a modulated wave excitation. An extra 1 row loose condition was tested at a position closer to the plate boundaries. Only one damage condition was induced for each tested configuration Damaged versus healthy strain spectra for each gage in rosette 2, using a 45 Hz high frequency drive. Very little nonlinearity is exhibited in the healthy condition, while the damaged condition shows high sideband content (+1 db for f1± components) xiii

14 4.7 Repeatable damage localization result for the 3 rows loose, damped plate configuration. Accurate estimates are shown over all forcing conditions Damaged versus healthy sideband amplitude ratios for the 1 row loose mid-plate damage condition, in the damped plate configuration. A peak nonlinear response is shown at 12 khz, where the f3 sideband shows an 8 db increase in all gages. Other frequencies show high increases in response, but not over all gages in the rosette. This led to selection of the 12 khz drive condition for further study Damaged versus healthy sideband amplitude ratios for the 1 row loose upper-plate damage condition, in the damped plate configuration. A peak nonlinear response begins near 12 khz, with the f 2 component showing a 2 db increase in the damaged condition. This is the highest increase shown over all drive conditions at this damage configuration Damaged versus healthy strain spectra for each gage in rosette 2, using a 12 khz high frequency drive for the upper-plate 1 row damage condition. Sideband amplitude increases are shown for all ± sidebands in the response Repeatable damage localization results for the (a) mid-plate and (b) upper plate 1 row loose damage conditions, in the damped plate configuration. Compared to the undamped plate, higher frequencies and adjustments in forcing are required to excite the high nonlinear response, and to localize on the damage Wavelength dispersion curves for the aluminum plate test bed. All damage sizes assessed in the damped and undamped configurations are marked according to their relative size and matching wavelength on the curve. The best PSL drive conditions are shown at 6 khz (undamped, 3 rows loose), 5 khz (undamped, 1 row loose), 4.5 khz (damped, 3 rows loose), and 12 khz (damped, 1 row loose). The majority of localization estimates were made using excitation frequencies near the critical frequency of the plate, at 4.8 khz, where radiation losses are the highest Example damaged versus healthy strain spectra for gage 1 in rosette 1, using a 25 Hz high drive frequency, with a UH-6 rotor blade passage frequency of 17 Hz. Components up to f8± were used for the total nonlinear estimate xiv

15 5.2 Repeatable damage localization results for the (a) 3 rows loose and (b) 1 row loose damage conditions. Each condition was assessed using the UH-6 blade passage frequency as a low drive source. A high frequency of 25 Hz was used in the 3 rows loose condition, while 3 Hz was used in the 1 row loose condition. These are comparable to previous 3 rows loose (Figure 4.7) and 1 row loose (Figure 4.11) results on the damped plate configuration UH-6 transmission frame test bed. The tested region of the airframe, a simulated skin-stiffener joint, is outlined in red Experimental setup for PSL testing on the airframe skin structure. A c-channel stiffener was added to the skin using existing bolt holes. The shaker was mounted to the nearest I-beam feature in a free-standing configuration. 2 strain rosettes were mounted on the.75 in thick skin to detect induced damage conditions. Both 6 loose (outlined in red) and 4 loose conditions (outlined in yellow) were tested Bending wavelength dispersion curve for the.75 in thick aluminum skin on the UH-6 upper cabin structure. The critical frequency of the aluminum skin is shown at 64 Hz. This drive condition was less crucial in the localization approach, due to the high damping of the built-up airframe structure Damaged versus healthy strain spectra for gage 1 in rosette 2, at the 6 Hz (1 V) high frequency drive condition. The damaged response is for the 4 loose mid-stiffener condition on the UH-6 upper cabin structure Damaged versus healthy strain spectra for the lower stiffener 4 loose damage condition on the UH-6 upper cabin structure. A high drive frequency of 45 Hz (1 V) exhibits the highest nonlinear response in the damaged condition. Broadband chaotic effects also appear in the response Strain responses from gage 1 of rosette 2, in the 4 loose lower-stiffener damage condition. A chaotic response is shown at.4 A of low frequency drive input, while the.1 A drive condition shows very little nonlinear response. More data points for forcing between these drive amplitudes may result in better angle estimates xv

16 5.9 Damage localization results for the (a) mid-stiffener (6 Hz at 4 V, 75 Hz at.4 A), and (b) lower stiffener (45 Hz at 4 V, 75 Hz at.6 A) 4 loose damage conditions on the UH-6 upper cabin structure. The lower stiffener condition shows some error, potentially due to the proximity of the damage and sensor rosette to the boundary of the skin-beam interface. The chaotic response in this damage condition may also degrade the angle estimates A.1 PSL position estimates for source position 3 (shown in green) on the aluminum plate A.2 PSL position estimates for source positions 5, 6 and 7 (shown in green) on the aluminum plate A.3 Transient response for rosette 3, filtered at the 3f/2 subharmonic. The first group arrival of the nonlinear component is near the.5 s. Gage 3 shows a peak amplitude of.4 µ-s A.4 Transient response for rosette 3, filtered at the 5f/2 subharmonic. The first group arrival of the nonlinear component is near the.5 s. Gage 3 shows a peak amplitude of.7 µ-s A.5 Transient response for rosette 3, filtered at the f/2 subharmonic, in the damped plate configuration. The first group arrival of the nonlinear component is near the.5 s. Gage 2 shows a peak amplitude of.14 µ-s A.6 Damaged versus healthy sideband amplitude ratios for the 3 rows loose damage condition, in the damped plate configuration. A peak condition is shown at 45 Hz, where a number of sideband components show a 1 15 db increase in the presence of damage. This drive frequency was chosen for further examination A.7 High frequency amplitude sensitivity for the modulated wave angle estimates, in the 3 rows loose, damped configuration. Angle estimates are accurate over the entirety of the forcing range, likely due to the very high sensitivity and low nonlinearity in the healthy condition A.8 Repeatability study for the modulated wave angle estimates, in the 3 rows loose, damped configuration. Steady-state drives consisted of 45 Hz (-5 db) and 75 Hz (-5.9 db) A.9 Damaged versus healthy strain spectra for each gage in rosette 3, using a 12 khz high frequency drive. Amplitude increases are shown for the f3 and f1+ sidebands xvi

17 A.1 High frequency amplitude sensitivity for the modulated wave angle estimates, in the 1 row loose, damped configuration. An accurate angle result is shown at high frequency drive amplitudes of 8.8 db and 1.6 db A.11 Low frequency amplitude sensitivity in the 1 row loose, damped plate configuration. Accurate localization results are obtained over the majority of the forcing range. The drive condition at -4.4 db was chosen for the repeatability study A.12 Repeatability study for the 1 row loose, damped plate configuration. Steady-state drives consisted of 12 khz (8.8 db) and 75 Hz (-4.4 db). 131 A.13 High frequency amplitude sensitivity for the modulated wave angle estimates in the 1 row loose, upper-plate damage condition. An accurate angle estimate result is shown at the lowest drive amplitude of 6.5 db A.14 Low frequency amplitude sensitivity for the upper-plate 1 row loose damage condition. Accurate localization begins at -3.7 db of drive amplitude A.15 Repeatability study for the upper-plate 1 row loose, damped configuration. Steady-state drives consisted of 12 khz (6.5 db) and 75 Hz (-3.7 db). Strain rosette 3 shows the least repeatable estimates, possibly due to its greater distance from the damage A.16 Damaged versus healthy sideband amplitude ratios for the 6 loose condition on the UH-6 upper cabin structure. A peak condition is shown at 45 Hz. Gage 3 shows low nonlinear increases across the testing range A.17 Damaged versus healthy strain spectra for rosette 1, using a 45 Hz high drive frequency. Gage 3 shows low signal compared to all other gages on the structure, indicating the gage is likely broken A.18 High frequency amplitude sensitivity for the 6 loose damage condition on the UH-6 upper cabin structure. Accurate estimates are shown for low drive amplitudes, though strain rosette 1 shows biased estimates due to the low signal from the 3-direction gage A.19 Low frequency amplitude sensitivity for the 6 loose damage condition on the UH-6 upper cabin structure. Accurate estimates are shown over the entire forcing range for strain rosette 2. Rosette 1 continues to show bias effects A.2 Repeatable localization result for the 6 loose damage increment, using drive conditions of 45 Hz (4 V) and 75 Hz (.4 A) xvii

18 A.21 Damaged versus healthy sideband amplitude ratios for the 4 loose mid-stiffener damage condition on the UH-6 upper cabin structure. A peak nonlinear condition is shown at 6 Hz A.22 High frequency amplitude sensitivity for the 4 loose mid-stiffener damage condition on the UH-6 upper cabin structure. Accurate estimates are shown for low drive amplitudes, up to 6 V high drive input A.23 Low frequency amplitude sensitivity for the 4 loose mid-stiffener damage condition on the UH-6 upper cabin structure. Accurate estimates are shown for low drive amplitudes, up to approximately.4 A low drive input A.24 Repeatability study for the 4 loose mid-stiffener damage condition on the UH-6 upper cabin structure. Steady-state drives consisted of 6 Hz at 4 V, and 75 Hz at.4 A xviii

19 List of Tables 1.1 Fatigue damage initiation sites for fixed-wing aircraft (data from Campbell and Lahey [8]) Fatigue damage initiation sites for rotorcraft (data from Campbell and Lahey [8]) Overview of CAN effects under a single tone excitation, compiled using dynamic modulus, stress and strain relations described in [24, 34] xix

20 Acknowledgments I would like to thank my advisor Dr. Stephen C. Conlon for all of his support throughout my undergraduate and graduate studies here at Penn State. Under his guidance I have learned so much about structural acoustics and dynamics, but also valuable life lessons that will stick with me throughout my career. I am also extremely grateful to Dr. George A. Lesieutre and Dr. Edward C. Smith for their support, in the form of teaching and research assistant funding provided through the Department of Aerospace Engineering, and the Vertical Lift Research Center of Excellence. I would also like to thank Richard Auhl for his technical insight, and Dr. Dennis McLaughlin for his advice along the way. Thank you to my family and friends for all of their love and support, and for being there in good times and bad. xx

21 Chapter 1 Introduction 1.1 Background Structural Health Monitoring (SHM) methods are gaining considerable support in the aerospace industry for their ability to detect and localize airframe damage. In both fixed wing and rotorcraft structures, SHM techniques can alleviate the dependence on frequent visual inspections, resulting in greater reliability, lower maintenance costs, and increased aircraft availability. While numerous SHM technologies are being developed in controlled laboratory environments, the successful integration of SHM in operational aircraft depends on a number of factors. The development of damage detection, localization, and automation procedures is critical for a practical implementation of SHM in airframe structures. Successful damage detection depends on effective measurement techniques, signal processing, and feature extraction. However, an airframe implementation must also satisfy aircraft design requirements. An onboard SHM system must perform its function with limited weight, power, and computing requirements, in order for the aircraft to perform its mission effectively. This research work aimed to evaluate nonlinear vibration based damage detection and localization techniques, with a focus on the use of minimal sensors and low weight impact on airframe structures. A primary focus was the development of potential automation procedures for an embedded SHM system, in an effort to extend the detection approach to real airframe applications. 1

22 1.1.1 Structural Health Monitoring SHM encompasses a wide range of research on the use of linear vibration, nonlinear vibration and guided wave methods for damage detection and identification. Farrar and Worden define damage as any changes introduced into a system that adversely affect its current or future performance [1]. In most industries, including aerospace, civil and mechanical disciplines, damage is detected over time using a schedule-based inspection and maintenance procedure. The transition from visual inspection methods to real-time sensor based monitoring represents a move towards Condition Based Maintenance (CBM). This philosophy relies on automated damage detection and localization to alert operators and maintenance crews of issues, so that repairs can be performed before damage propagates to the point of failure. For any SHM system, there are some fundamental principles that must be considered. Concisely listed by Worden et al. [2], these can be outlined as follows: All materials have some inherent defects. Embedded SHM must be able to distinguish between damage and an inherent material flaw, which may not necessarily affect performance of the system as a whole. The evaluation of damage requires a comparison of system states, namely a damaged state compared to a healthy baseline. The existence and location of damage may be determined without prior data in the damaged condition. However, characterization of the type and extent of damage requires prior classification of data in the damaged condition. Sensors alone cannot measure damage. Intelligent feature extraction from measured data is required in order to detect and characterize damage. In addition, the more sensitive a measurement is to damage, the more sensitive it is to changes in operational or environmental conditions, requiring even more intelligent feature extraction to interpret the data. The damage size of interest is inversely proportional to the excitation frequency required to detect the damage. The size and time frame associated with damage propagation dictates the requirements of the SHM system. 2

23 The more sensitive an algorithm is to damage, the more sensitive it is to noise in the system. These principles offer some general guidelines regarding sensor requirements, signal processing, and selection of drive frequency. Over the years, research has shown that low frequency methods are not generally a good indicator of small scale localized damage [3, 4], such as fatigue cracks. This is true because the structural wavelengths of global modes are very large compared to the size of the damage, and the damage tends to follow the displacement of the modes at low frequencies. Furthermore, modal parameters are highly dependent on environmental factors such as temperature, and can show large changes over time, even for an undamaged system. High frequency methods utilizing ultrasonic vibrations and guided waves are much more sensitive to local damage. In general the sensitivity of the method increases with increasing excitation frequency, though nonlinear structures and materials can be sensitive at much lower frequencies [2]. This makes high frequency nonlinear methods particularly attractive for detecting small-scale damage, such as fatigue damage found in airframe structures Application to Airframe Structures Fatigue plays a key role in the design of airframes. According to Pitt and Jones [5], three main design approaches have typically been used in ensuring the safety of aircraft. The first is known as the safe-life approach where a component is assumed to be safe for a prescribed number of load cycles, provided it stays within designed load limits. At the end of this period the component is automatically replaced, regardless of condition. As a result, many components are over-designed to meet the prescribed service life and are replaced well before the component is actually unusable. This leads to higher weight, waste of materials, and design inefficiencies, which are costly over the lifetime of an aircraft. A fail-safe design approach alleviates some of these issues, by ensuring that a component is able to withstand some damage without catastrophic failure of the entire structure. This leads to more lightweight components, but the approach generally includes redundancy and crack arresting features in the design, so that damage can be visually detected and repaired before failure occurs. Unfortunately, predicting which areas of the structure are most susceptible to fatigue damage is a difficult task, so additional load path features are included in the design. 3

24 This also leads to inefficiency over the lifetime of an aircraft. The majority of current fatigue design is carried out using a damage tolerance approach, where a structure is assumed to have an initial flaw, and that flaw is allowed to grow throughout the service life. Inspection intervals are set based on analytical knowledge of the fatigue life of the structure, supported by rigorous experimental testing. Continued inspection throughout airframe fatigue testing allows designers to change aspects of the structure, or to set inspection intervals for maintenance crews in the field [6]. Both civil and military aircraft are subjected to frequent visual inspections, according to the requirements set forth by their component fatigue life estimates. In order to reach sections of the airframe that are difficult to inspect, components are often disassembled and subjected to Non-Destructive Evaluation (NDE) techniques such as ultrasonics, dye penetrant, and eddy current evaluation. As unexpected damage occurs, these inspections become more frequent, resulting in costly downtime for the aircraft. Despite these efforts, damage can initiate and propagate between inspection cycles, reaching dangerous levels if overlooked. Fatigue damage can stem from flaws throughout various stages of the structure life cycle, including during manufacturing, operation, and even through the acts of inspection and maintenance. It is believed that fatigue contributes to 6% of all aircraft component failures [7], and therefore, detection of fatigue damage is a high priority for aircraft in service. In general, fatigue damage occurs in the presence of high stress concentrations. Stress concentrations are common in airframe structures, especially at joints, where fasteners and bond lines are subjected to high cyclic loading in operation. Over time, bolts and rivets can loosen, transferring loads to nearby fasteners, and causing fatigue cracks to initiate and propagate at hole locations. A worldwide survey of serious fatigue related accidents, by Campbell and Lahey [8], highlighted major trends of fatigue failures in both fixed wing and rotorcraft structures. Table 1.1 shows fatigue initiation sites for fixed-wing aircraft, where fasteners and fastener holes accounted for a combined 4% of accidents. Table 1.2 shows similar statistics for rotorcraft, where a combined 36% of fatigue initiation sites occurred at fastener locations. These trends illustrate the importance of detecting fatigue damage at an early stage in propagation, a task that could be carried out most efficiently using an SHM system. Other fatigue studies have shown comparable results for both civil and military aircraft. For instance, a major airframe fatigue test on a Tornado fighter aircraft 4

25 Table 1.1: Fatigue damage initiation sites for fixed-wing aircraft (data from Campbell and Lahey [8]) Initiation Site Accidents % Bolt, stud or screw Fastener hole or other hole Fillet, radius, or sharp notch Weld Corrosion 43 1 Thread (other than bolt or stud) 32 7 Manufacturing defect 27 6 Scratch, nick, or dent 26 6 Fretting 13 3 Surface or subsurface flaw Improper heat treatment 4.9 Maintenance-induced crack 4.9 Work-hardened area 2.4 Wear 2.4 Total 449 Table 1.2: Fatigue damage initiation sites for rotorcraft (data from Campbell and Lahey [8]) Initiation Site Accidents % Bolt, stud or screw Fillet, radius, or other stress concentration Corrosion Fastener hole or other hole 12 1 Fretting 1 8 Manufacturing defect or tool mark 9 7 Brinneling, galling or wear 7 6 Thread (other than bolt or stud) 4 3 Weld 3 2 Subsurface flaw 3 2 Softened condition or subsurface decarburization Surface scratch or damage Total 125 5

26 revealed that 7% of accrued airframe damage was in the form of fatigue cracks, with 53% of that damage stemming from fastener locations [9]. A summary of in service Boeing 747s identified 714 cracks in 61 aircraft over a 3 year period, with 91% of these cracks stemming from fastener locations or changes in geometry in the fuselage structure [9]. A recent study out of AugustaWestland compared damage causes and initiation sites from maintenance logs with those presented by Campbell and Lahey in Figure 1.1 shows a comparison of fatigue damage locations for both surveys [1]. Notably, in the AugustaWestland maintenance logs the airframe accounted for 3.3% of fatigue damage, compared to 8.4% in the Campbell and Lahey survey. The main reason is the difference in focus between studies, since the AugustaWestland survey emphasized normal repairs over catastrophic failures. Regardless, both surveys highlight the importance of early fatigue damage detection in airframe structures. SHM technologies can serve to detect and localize on damage, while reducing the time spent in maintenance and visual inspections. Figure 1.1: Fatigue damage initiation sites, documented by (a) AugustaWestland [1] and (b) Campbell and Lahey [8]. Two current military assets that could benefit from SHM technologies are the UH-6A Black Hawk [11], and OH-58D Kiowa Warrior [12]. Figure 1.2 shows these airframe structures, with typical damage hot spots highlighted. Loose fasteners and fatigue cracks are common on the UH-6 upper cabin structure, where the airframe 6

27 is subjected to the high cyclic loading of the main rotor system. On the OH-58, fatigue damage is a prominent concern at rivet lines and joints on the structure, particularly in the golden rivet region near the tail rotor, where current visual inspections are focused. This region of the airframe has been a typical source of fatigue related problems throughout every variant of the aircraft. An embedded SHM system could allow for improved damage detection and localization at damage hot spots, as well as global detection capability, reaching areas of the airframe that would be difficult to inspect visually. As new aircraft are developed, SHM technologies could be incorporated in the airframe during the design stages. This could pave the way for lighter, more efficient designs, with less dependency on the traditional damage tolerance approach. Accurate, real-time damage detection could be performed, ensuring efficient maintenance procedures throughout the service life of the aircraft. Figure 1.2: UH-6A Black Hawk upper cabin and OH-58D Kiowa Warrior tailboom, with common fatigue damage initiation sites highlighted. An embedded SHM system could detect damage at these hot spots in real-time, alleviating the costly downtime associated with visual inspections. 7

28 1.2 Linear Vibration and Guided Wave Methods The concept of using structural vibration to diagnose the presence of damage has been used for hundreds of years. An early example is the detection of damaged train wheels by hitting the wheel with a hammer and listening to the response [13]. In principle this is a linear vibration based damage detection method, where modal properties of a structure or component, such as resonance frequencies and damping, are tracked over time to indicate when damage occurs. The onset of damage has the effect of shifting the natural frequencies of the structure, altering damping parameters, and changing the characteristic mode shape. The problem with linear vibration methods is that global modes of the system are relatively insensitive to small changes in the structure, such as local changes in stiffness brought on by fatigue damage. In addition, modal parameters are often more sensitive to environmental factors like temperature and humidity. This causes difficulties when attempting to diagnose the presence of damage in the system [13]. Being global properties of the structure, modal parameters also offer little benefit for localization of the damage. Guided wave methods have been the subject of extensive research for use in NDE and SHM technologies [14 16]. These methods typically use a pitch-catch or pulse-echo approach to send and receive signals. Features of these signals are then extracted and used to identify the presence and location of damage. A typical implementation is shown in Figure 1.3, where a source is used to send out a transient tone burst signal. The damage acts to scatter the waveform, resulting in two distinct wave groups, and the time record of the scattered signal is received at various sensors on the structure. Using a known wave speed and group arrival time at the receivers, a damage location can be estimated. Ultrasonic guided wave approaches typically require a dense grid of sensors and actuators to detect and localize on damage in a specific region of a structure. In a study by Ihn and Chang [17], a 462 mm riveted lap joint was monitored using 36 piezoelectric sensors/actuators, and damage was detected in a.76 m by.76 m composite panel with the use of 3 embedded piezoelectric sensors/actuators. This high density of sensors may not be practical for a real airframe SHM implementation, where weight and power requirements are critical. Recent studies have aimed to develop guided wave approaches on representative airframe structures, including the OH-58D [18, 19] and Bell 47 [2]. However, 8

29 Figure 1.3: Traditional guided wave approach. A tone burst signal is sent by a source and received by various sensors on the structure. A scattered signal shows the presence of damage, and damage can be localized using the associated time of flight of the scattered waveform. In general, a complex network of actuators and sensors is required for accurate detection and localization. damage detection results have generally been limited to lab specimens in a controlled environment. In a flight tested OH-58D implementation, a SMART Layer containing 8 piezoelectric sensor/actuators was installed to specifically monitor the golden rivet region of the tailboom [18]. This sensor configuration is shown in Figure 1.4. Designed for a specific use, this configuration represents a typical high sensor density approach, which is difficult to implement in a more widespread detection scheme, simply due to the weight and power requirements necessary to support the system. In addition, the complexity of the sensing network requires careful data management, and poses concerns for long term reliability of the system. 9

30 Figure 1.4: SMART Layer sensor installed on an OH-58D tailboom in order to monitor the golden rivet region of the structure. The layer contains 8 piezoelectric sensor/actuators (figure from Ref. [18]). Guided waves are also subject to a number of difficulties in practice, as outlined by Meo and Mattei [21]. Signal-to-noise problems are common and results are often difficult to reproduce. In complex structures, pure guided wave modes are difficult to propagate due to reflection and absorption through the geometry. Furthermore, the dispersive nature of the propagating waves results in considerable attenuation of the group waveforms over a distance, making received signals difficult to interpret. A detection approach using nonlinear vibrations may be more attractive for a practical implementation. 1

31 1.3 Nonlinear Vibration Based Damage Detection Overview Nonlinear wave spectroscopy based methods, using Contact Acoustic Nonlinearity (CAN) effects, have been studied for use in NDE and SHM applications. Studies have used both a single active interrogation [22, 23] approach and a Nonlinear Wave Modulation Spectroscopy (NWMS) method [24 27] to excite a nonlinear response at the damage location. The damage acts as a nonlinear scatter of the propagating wave, with nonlinear frequency components following a linear wave propagation path from the damage. Nonlinear detection methods have proven effective on both metallic and composite structures [28, 29]. An illustration of both single tone and NWMS methods is shown in Figure 1.5. In a healthy state, only the active interrogation frequencies are shown in the strain response of the structure. However, in the presence of damage, energy from the single active drive source leaks into bifurcations of the drive frequency at subharmonics, ultra-subharmonics (f/2, 3f/2, nf/2,...) and higher harmonics (2f, 3f, nf,...), with the damage exhibiting a local parametric resonance effect at these frequencies. An analogous effect occurs in the presence of two active drive frequencies. In this case the low frequency acts to modally exercise the damage location, while the high frequency probing wave penetrates the disbonded interface. The opening and closing of the interface scatters energy from the two drive frequencies into nonlinear sideband frequency components (f high nf low ). In a practical implementation, some nonlinearity is always present due to harmonic distortion of the active drive system, intrinsic material nonlinearity, and changes in stiffness over the geometry of the structure (changing stress-strain dependencies with changing geometry). However, by comparing the growth of nonlinear components throughout healthy and damaged conditions, information about the state of the damage can be extracted. Nonlinear components can be tracked in order to quantify the extent of the damage, and to determine the location of the damage. 11

32 Figure 1.5: Example healthy strain amplitude in the presence of a single tone excitation (A), damaged response exhibiting higher harmonics, subharmonics, and ultra-subharmonics of the drive frequency (B), healthy response in the presence of two interrogation frequencies (C), and damaged response showing multiple plus and minus sidebands centered around the high drive frequency (D). 12

33 1.3.2 Theoretical Development Though a complete theoretical derivation of the many nonlinear vibration phenomena is beyond the scope of this thesis, a number of researchers have attempted to provide a framework for modeling nonlinear effects. In general, these effects can be classified as stable and unstable. Stable effects include higher harmonics and wave modulation, consequences of the asymmetric material stiffness at the damage location. Unstable effects include subharmonics, ultra-subharmonics, ultra-frequency pairs and chaotic responses, which are a result of the local parametric resonance of the damage itself Higher Harmonics and Wave Modulation Nonlinear effects are present in most materials, stemming primarily from a nonlinear relation between stress and strain. The dynamic stress-strain behavior of solids can be expressed as: σ = E(ε, ε)dε, (1.1) where σ is the material stress and the modulus E is a function of the strain ε and strain rate ε (where ε = dε/dt) [24]. E can be expressed in its nonlinear hysteretic form: E(ε, ε) = E {1 βε δε 2 α[ ε + ε(t)sign( ε)] +...}, (1.2) where E is the linear elastic modulus, ε is the local strain amplitude, sign( ε) = 1 if ε >, and sign( ε) = 1 if ε <. β is the first order nonlinear coefficient, δ is the second order nonlinear coefficient, and α is a parameter measuring the material hysteresis. The overall result of these nonlinear effects is a distinct deviation from the typically linear stress-strain curve, where the modulus, and therefore stress, are nonlinear functions of strain. Combining Equations 1.1 and 1.2, dividing out the constant material modulus E, and representing all hysteretic nonlinear terms as ε HN yields an integral expression for the nonlinear strain response ε out as a function of the input strain ε in [3]: ε out = [1 βε in δε 2 in ε HN ]dε. (1.3) The classical and hysteretic nonlinearity terms can be integrated separately for further analysis. Hysteretic terms can be modeled in a number of ways [31], and solved quasi-analytically [32], or numerically [33], depending on the complexity of 13

34 the material response. However, an analytical solution can be found for the classical terms, generating higher harmonics and sidebands in the strain response. Integrating the classical nonlinear terms in Equation 1.3 results in the expression: ε out = ε in βε2 in 2 δε3 in 3, (1.4) where ε in can be explicitly defined as one or two input sine waves (or multiple frequency components), with frequencies f 1 and f 2, and amplitudes A 1 and A 2 : ε in = A 1 cos 2πf 1 t + A 2 cos 2πf 2 t. (1.5) Inserting Equation 1.5 into 1.4, expanding the exponential expressions, and applying trigonometric identities results in an expression for the strain response, incorporating multiple higher harmonics and sidebands. In Equation 1.4, the squared term gives rise to the first higher harmonic (2f 1 and 2f 2 ) and first sideband components (f 2 ±f 1 ). The cubic term results in the second higher harmonic (3f 1 and 3f 2 ) and second order sideband components (f 2 ± 2f 1 ). The fundamental frequency amplitudes are shown to influence each other. The first harmonic amplitudes show a quadratic relation to their respective fundamentals, while the second harmonics show a cubic relation. Classical nonlinear theory predicts that the first order sidebands will have amplitudes proportional to βa 1 A 2, while the second order sidebands will be proportional to δa 2 1A 2 and δa 2 2A 1 [3]. For a purely hysteretic material, no even harmonics exist, and each odd harmonic will have a quadratic dependence on the fundamental. The pure hysteretic model predicts second order sidebands dependent on the nonlinear hysteretic interaction, with amplitudes proportional to αa 1 A 2 [24]. Solodov offers a different approach, modeling a bilinear stiffness relation [23], σ = E [1 H(ε)( E /E )]ε, (1.6) where H(ε) is the unit step function, and E = [E (dσ/dε) ε> ]. The physical implication of this expression is an intact linear stiffness when the material is in compression and a decreased stiffness when the material is in tension, signifying an opening of the damaged interface. The result is a periodic shifting of intact and decreased stiffness, and a number of higher harmonics in the response. Similarly, for a wave modulation approach, Solodov describes the low frequency excitation as 14

35 a switch for the stiffness modulation with frequency f 1. The induced stress at the mixing frequencies is then dependent on the amplitude of the high frequency f 2 probing wave and the change in stiffness induced by the low frequency exercising wave [34]. The result in the frequency spectrum is a distinct cascade effect of numerous nonlinear sidebands, centered around the high drive frequency. Summaries of modeled nonlinear effects from the literature, specifically those described by Van Den Abeele et al. [24] and Solodov [34] are shown in Table Subharmonics, Ultra-Subharmonics, Ultra-Frequency Pairs, and Chaotic Response At some drive conditions, material damage such as fatigue cracks can exhibit local nonlinear resonance modes. These unstable modes can be physically interpreted as half-frequency and combination frequency decays of the high frequency drive. In subharmonic generation, the damage essentially acts as a nonlinear oscillator. The characteristic frequency is dependent on a linear stiffness, and an associated mass of the material inside the damaged region [23]. This gives rise to subharmonics and ultra-subharmonics of the drive frequency f. If the nonlinear system is modeled as a set of coupled nonlinear oscillators, there is a condition where the drive frequency is equal to the summation of the two nonlinear resonance frequencies, yielding ultrafrequency pairs centered around the subharmonics and higher harmonics [35]. Past a certain threshold of drive amplitude, subharmonics and ultra-frequency pairs grow in amplitude and number, until an overall temporal instability is developed. The nonlinear components fluctuate in amplitude and phase until an overall broadband chaotic response is shown [36]. Knowing the dependence of the coupled nonlinear oscillator model on drive frequency and amplitude, nonlinear regimes in the response can be summarized as in Figure 1.6, where ν is the drive frequency, and ω 1 and ω 2 are the nonlinear resonance conditions [37]. There is clearly a frequency and amplitude dependent threshold where the response transitions from the stable higher harmonic and wave modulation (HH & WM) regime, to subharmonics/ultra-subharmonics (USB), ultra-frequency pairs (UFP), and eventually chaos. These effects were observed experimentally throughout the course of this research. 15

36 Table 1.3: Overview of CAN effects under a single tone excitation, compiled using dynamic modulus, stress and strain relations described in [24, 34]. 16

37 Figure 1.6: Nonlinear regimes associated with the coupled nonlinear oscillator model of a damaged material response, where the nature of the nonlinear response is dependent on the drive amplitude and drive frequency ν (figure from [37]) NDE Applications Nonlinear vibration based methods have been developed for a number of NDE applications. An early example from 1975 is a United States patent describing the use of simultaneous low and high frequency vibrations for fatigue crack detection, now known as the NWMS, or modulated wave approach [38]. Aforementioned studies by Van Den Abeele, Johnson and Sutin (2-21) used wave modulation for material and automotive part diagnostics [24, 25]. Techniques were developed using two discrete frequencies, as well as a high frequency and impact modulation. In this method, the modal excitation of the structure is provided by a hammer impact, resulting in sideband content generated by all the structural modes. An integration of sideband energies is used to quantify the extent of the damage with a healthy baseline. Donskoy et al. (21-23) used modulated wave techniques for detection of fatigue cracks in metals [26, 27]. Meo and Zumpano (25) applied similar techniques to a laminate panel with a honeycomb core [29], while Aymerich and Staszewski (21) successfully applied the technique for detection of impact damage in a composite laminate plate [28]. The success of modulated wave techniques for a wide array of materials is an important step towards applications in aerospace structures, which often incorporate a range of metallic and composite materials. 17

38 Other research has aimed to improve modulated wave techniques by studying different drive methods and experimental factors affecting detection capability. Zaitsev, Gusev and Castagnede used an amplitude modulated low frequency drive, citing potential benefits over traditional wave modulation from the time dependent sideband response [39]. A 211 study highlighted the importance of using higher order nonlinear interactions in modulated wave techniques [4]. Specifically, the atomic nonlinearity of an interrogated material was shown to be strong in both healthy and damaged conditions, resulting in prominent first order sideband content. Higher order sidebands (f high ± 2f low, 3f low,...) were shown to be a better indicator of damage, because the background nonlinearity had little effect on these components. While few studies have aimed to use wave modulation in an embedded system, Courtney describes advanced signal processing techniques, effects of transducer positioning, nonlinear effects from boundary conditions, as well as a method for automated scanning using a modulated wave approach [41]. The multiple mode method uses a range of low and high frequencies and scans over all combinations to identify the highest nonlinear response. The damage level is then determined by taking into account the increase in nonlinear content across all the modes Penn State Airframe SHM Applications In past research conducted at the Pennsylvania State University, CAN based damage detection methods were developed for embedded airframe SHM applications. Nonlinear wave spectroscopy techniques were used to detect loose fasteners and fatigue cracks in metallic structures [42], as well as delaminated stiffener damage in a composite test bed [43, 44]. These methods were successfully translated to a UH-6A upper cabin structure [45] and OH-58D tailboom [12, 44]. High sensitivity detection results were obtained for damage conditions sized on the order of damage barely visible during typical visual inspections. Further studies characterized the effects of varying load conditions on the nonlinear detection feature [46], in order to evaluate the technique for use in operational aircraft. In each study, damage sensitivity was enhanced by fusing strain rosette and in-plane acceleration measurements into a single power flow related quantity, the Nonlinear Structural Surface Intensity (NSSI) metric. Results for a previous study on the stiffened plate test bed (outlined in Section 2.1 and used throughout this 18

39 research) are shown in Figure 1.7 [46]. For the same drive condition over three damage increments, the strain based measurements show only 7 db sensitivity at the largest damage increment, while the NSSI quantity shows 3 db of detection sensitivity. While high sensitivity detection was achieved in previous work, the topic of localization was not addressed. NLS (db re 1 µ S) NLS x NLS y NLS 45 NSSI (db re 1 W/m 2 ) Damage Increment (Rows Loose) (a) Nonlinear strain detection result Damage Increment (Rows Loose) (b) NSSI detection result. Figure 1.7: Damage detection results using both nonlinear strain and NSSI metrics on the stiffened aluminum plate test bed [46]. Results show the detection benefits of the NSSI approach. Localization of damage was not addressed in previous studies. Physically, the NSSI feature is used as a measure of the power flow due to the nonlinear signature of the damage, at discrete points on the structure. The NSSI sensor suite, incorporating 3 piezoelectric strain sensors and 2 uniaxial accelerometers, is shown in Figure 1.8. In the time domain, structural intensity is related to a product of the stress and velocity of the wave propagation. In practice, a frequency domain method was used to calculate the NSSI quantity. Acquired acceleration data was numerically integrated to yield the x and y velocities, u x and u y. Strain rosettes were used to measure the normal strains ε x and ε y, as well as the shear strain γ xy. The complete NSSI formulation is shown in Equations , where f NL represents the nonlinear frequency component of interest, f int represents the use of upper and lower integration bounds in the frequency domain, and the quantity G xy is the cross-spectral density of quantities x and y. In these equations stress-strain relations have been utilized to convert spectral strain measurements to stresses, and the operator Re signifies the real part of the complex quantity. Since NSSI is a vector quantity, a vector summation of x and y components is used to yield the NSSI magnitude. Note that 19

40 the expressions also include a summation to account for nonlinear energy at multiple frequency bands, such as the subharmonic response of a single-tone excitation, or the sideband response of a wave modulation approach. NSSI x = ( G Re f NL +f int [ f NL f int 2 1 ν ( Gεxu x + ν G ) ] εyux + Gγxyuy df) (1.7) NSSI y = ( G Re f NL +f int [ f NL f int NSSI = 2 1 ν ( Gεyu y + ν G ) ] εxuy + Gγxyux df) (1.8) (NSSI x ) 2 + (NSSI y ) 2 (1.9) The global detection capability of nonlinear wave spectroscopy methods has been verified using minimal sensors and actuators, detecting simulated damage on real airframe test beds. Both single tone and NWMS methods showed promising detection capability, though the single tone method was much more selective to drive conditions, due to the instability of the self-modulation subharmonic effect. It was concluded that the NWMS approach, with its stable nonlinear response, would be most conducive to development of automated routines in embedded SHM technologies [12, 44]. Figure 1.8: NSSI sensor suite featuring 3 piezoelectric strain sensors in a rectangular rosette configuration and 2 uni-axial accelerometers. The inherent data fusion of NSSI results in a high sensitivity detection metric. 2

41 1.4 Damage Localization In addition to detecting the presence of damage, an important component of SHM is localization of the damage. In guided wave studies this is typically accomplished using the scattered signature of the damage and known propagating wave speeds. Knowing the time of flight of the scattered waveform, the distance to the damage can be calculated and a position can be synthesized using information from a number of sensors [17]. The technique can be very accurate for simplified plate-like structures, but for complex structures calculation of the necessary wave speed information is often a difficult task, due to the complicated boundary conditions and interfaces [21]. While a baseline measured wave speed can be used to detect changes in signal amplitude and time of flight, in practice the guided wave technique requires a number of sensors/actuators working in conjunction to monitor a specified area of the structure. This can add considerable weight and computing requirements for an embedded system, especially when employing guided waves in a global detection role. Other vibration source localization methods have been explored, detecting impacts on composite structures using strain rosette based measurements [47, 48]. These methods were previously used in numerical studies to accurately predict the position of damage, by focusing on higher harmonics in the strain response, an effect of the asymmetric stiffness at the damage location [11]. The experimental implementation of this Principal Strain based Localization (PSL) approach was a primary goal of this research. Since previous experiments in NSSI damage detection used rectangular rosette configurations and similar processing methods, the PSL approach represented a logical step towards a real airframe implementation for damage detection and localization, building upon past research in NSSI damage detection techniques. The PSL method depends on the inherent directional response of strain measurements to predict the angle corresponding to the path of an incident wave traveling through a rosette. The signal voltage acquired through a single strain gage depends on the direction of an incident strain wave, as shown by V S 1 ε 11 + S 2 ε 22, (1.1) where S 1 represents the longitudinal sensitivity of the gage, S 2 represents the transverse sensitivity, and ε 11 and ε 22 are the components of the incident strain wave in the 1 21

42 and 2 directions [47]. These components can be defined explicitly by transforming the incident strain amplitude ε into the gage axis: ε 11 = ε cos 2 θ, (1.11) ε 22 = ε sin 2 θ. (1.12) In these equations, θ is the angle of the incident strain wave, referenced to the longitudinal (sensitive) axis of the gage. Note that typical transverse sensitivities for the gages used in this study were on the order of 5%, according to the manufacturer [49]. Using strain signal amplitudes for the frequency of interest, and assuming an incident plane wave traveling through the rosette, the maximum principal strain angle is calculated: φ = 1 2 tan 1 γ xy ε x ε y. (1.13) In this expression, γ xy is the calculated rosette shear strain, while ε x and ε y are the strains in the x and y directions, respectively. If the system directional axes are aligned with the rectangular rosette axes, the normal and shear strain components can be written as shown in Equations (1.14) (1.16), where ε 1 is the gage, ε 2 is the 45 gage, and ε 3 is the 9 gage [5]. ε x = ε 1 (1.14) ε y = ε 3 (1.15) γ xy = 2ε 2 ε 1 ε 3 (1.16) Similar expressions can be written for a delta rosette configuration (shown alongside a rectangular rosette in Figure 1.9). The delta rosette, because of the wider spacing between gages, potentially yields higher directional accuracy [5]. Though its use is sometimes limited based on its slightly larger footprint. Equations are used to calculate normal and shear strain components for this configuration. ε x = ε 1 (1.17) ε y = [2(ε 2 + ε 3 ) ε 1 ]/3 (1.18) γ xy = 2(ε 2 ε 3 )/ 3 (1.19) 22

43 Extracting strain amplitudes of the nonlinear components in each gage response, the resulting PSL angle estimates provide an estimate of the damage (or virtual source) location, whose signature is the nonlinear response. A visualization of the PSL angle estimate for a modulated wave response is shown in Figure 1.1. A steadystate excitation at f low and f high propagates from the source location, scattering into nonlinear sideband components at the damage. The low and high frequency sources, shown in a collocated configuration, can be placed at different locations on the structure. It is assumed damage contributes energy to all nonlinear components, so each sideband response for each strain gage must be considered in the localization approach. In practice, the experimental PSL method is subject to a number of factors, which must be considered when evaluating position estimates based on the measured principal strain angles. Most importantly, a minimum of 2 strain rosettes is required to obtain enough information for localization. Because the method is dependent only on measured strain amplitudes, only the angle of the wave propagation is determined by a single rosette. The direction of the wave propagation from the source (and therefore the source position) is only determined by obtaining a second rosette measurement and determining the intersection points of the two vectors, oriented at the corresponding maximum principal strain angles. Multiple rosette estimates can be used to increase confidence in the measured source position. For this study, standard principal strain measurement practices (outlined in [5]) were followed to determine the angle corresponding to the maximum principal strain value. This prevented potential 9 errors from angle estimates aligned at the minimum principal strain angle. 23

44 Figure 1.9: Comparison of rectangular and delta strain rosette configurations. These are the two most common rosettes used in measurements of strain for principal axis calculations. Figure 1.1: Physical representation of the damage as a virtual source in the system. Energy from the two collocated active drive frequencies is scattered into nonlinear components. Strain measurements of the nonlinear amplitudes provide information about the direction of the incoming damage induced signatures. 24

45 1.5 Objectives and Outline Research Objectives This research focused on the development and experimental implementation of a nonlinear damage detection and localization method, suitable for embedded SHM systems. In this work, minimal sensors and actuators are used to detect and localize on damage, in an effort to provide a framework for a lightweight and low power embedded Structural Health Monitoring (SHM) system. The resulting strain based localization approach can use as little as 6 sensors, compared to the high sensor density of traditional guided wave methods. An emphasis is placed on algorithms for an automated detection technique, using nonlinear wave spectroscopy methods. Key components of the automation routines involve selection of drive conditions to elicit the nonlinear response at the damage, and an evaluation of force levels and their effect on the localization approach. Single tone interrogation methods are explored using both transient and steady-state excitations. The steady-state wave modulation method is favored over the single tone approach, due to its stable nature, and low sensitivity to small changes in drive conditions. To summarize, specific objectives for this research included: Experimental evaluation of the Principal Strain Localization (PSL) routine on typical skin-stiffener airframe damage conditions. Development of nonlinear wave spectroscopy data reduction and processing schemes for an embedded SHM system. Selection of optimal active drive conditions, based on a direct comparison of healthy and damaged system states. Determination of required force levels for detection and localization of damage using nonlinear methods, and other experimental factors affecting the approach. Evaluation of potential automation algorithms for the nonlinear detection and localization approach. Previous research has shown the detection capability of nonlinear vibration based methods on prototypical test beds and airframe structures, while numerical studies 25

46 have incorporated the PSL technique to localize on nonlinear signatures from the damage. However, the PSL technique has not been implemented in experiments, and algorithms for automation of the nonlinear approach have not previously been explored. Results presented in this thesis aim to address these components of nonlinear vibration based SHM, furthering development of the methods for use in current and future aircraft designs Thesis Outline This thesis is organized into 6 chapters. Chapter 2 contains an introduction to the test beds, sensors, and data acquisition used throughout the study. Processing schemes are introduced for the various interrogation schemes, including single tone, transient and steady-state, and steady-state wave modulation. Initial localization testing is explored. Chapter 3 contains a summary of damage detection and localization results obtained on a stiffened aluminum plate test bed. Chapter 4 explores the effects of damping treatment on the plate test bed and its effect on damage localization routines. Chapter 5 explores real airframe applications, using the same techniques developed on the simplified test bed. Chapter 6 provides conclusions on the detection, localization, and automation procedures developed throughout this research, with suggestions for future work. 26

47 Chapter 2 Experimental Setup and Methods Development 2.1 Stiffened Plate Test Bed A stiffened aluminum plate test bed was used to develop the experimental damage detection and localization methods. The test bed served as a representation of a typical skin-stiffener joint found in rotorcraft and fixed wing airframe structures. The 775 aluminum alloy plate, shown in Figure 2.1, had dimensions of 89 cm x 58 cm x.25 cm. An aluminum stiffener was attached near the center line of the plate, using 11 rows of 1-32 fasteners, at 5 cm spacings along the joint. The stiffened plate was mounted in a heavy steel fixture to provide stable and repeatable boundary conditions. A damaged joint condition was induced by loosening various rows of fasteners along the joint line. This simulated damage caused the characteristic clapping effect of CAN under an active vibration interrogation. The plate was instrumented with three piezoelectric strain sensor rosettes in a rectangular configuration. Each rosette was made up of commercially available PCB Piezotronics strain sensors (model 74B2). Rosette 1 was located approximately 18 cm from the left and upper edges of the plate, while Rosette 3 was located the same distance from the right and lower edges of the plate. Rosette 2 was located approximately 5 cm closer to the stiffener and 6 cm higher in the lower left region of the plate. This position was chosen to mitigate effects of symmetry in the sensing grid, since in a real application it is unlikely that damage would initiate at an equal distance from all sensors. To provide two active drive sources for the structure, a Wilcoxon 27

48 F4/F7 collocated shaker assembly was mounted behind the plate, approximately 18 cm from the upper edge and 2 cm from the right edge. Force levels from the two shakers were monitored using an impedance head (PCB Piezotronics model 288D1) at the interface between the stinger and plate. Figure 2.1: Stiffened aluminum plate test bed (775 aluminum alloy, 89 cm x 58 cm x.25 cm), instrumented with 3 piezoelectric strain sensor rosettes (PCB Piezotronics 74B2). A collocated low/high frequency shaker assembly (Wilcoxon F4/F7) provided two active drive sources. A damaged joint condition was induced by loosening rows of fasteners along the joint. National Instruments (NI) data acquisition (DAQ) hardware was used to acquire all signals from the Integrated Circuit Piezoelectric (ICP) powered strain sensors. A schematic of the complete setup is shown in Figure 2.2. The high frequency source was driven using either the Tektronix AFB3123 function generator for steady-state excitation, or an NI-6733 PXI output card for a transient signal. The signal was amplified using the Crown XTi 2 amplifier, passed through the Wilcoxon N7C impedance matching network, and sent to the F7 high frequency shaker. The low frequency excitation signal was provided by a compact DAQ (cdaq) NI-9263 output card, amplified using the Crown amplifier, and passed to the F4 electromagnetic shaker. 28

49 Steady-state signal amplitudes were monitored in real-time using voltmeters, while time data was acquired using NI-4472 PXI input cards (2 x 8 channels). Proprietary LabVIEW codes were used for generating waveforms and acquiring the raw time data. Figure 2.2: Flowchart of data acquisition, sensor and actuator hardware used throughout this study. 2.2 Single Tone Data Processing Techniques Strain time records were acquired for a variety of excitation methods, including steadystate and transient single tone, and steady-state wave modulation. A systematic data processing routine was developed for each drive method in order to extract strain information for the PSL approach. Initial efforts focused on single tone excitations, and the generation of sub-harmonics from the local parametric resonance of the damage. While a steady-state excitation was shown in past studies to yield high signal-to-noise nonlinear signatures, the transient method was expected to provide additional information about the time of flight of the nonlinear signature and the 29

50 level of reflections from the plate boundaries. The data processing algorithm used to extract PSL estimates from both single tone transient and steady-state time records is shown in Figure 2.3. Using a steady-state excitation, strain time records were passed through a Fast Fourier Transform (FFT) algorithm and amplitudes were extracted for each gage in a rosette, using a peak finding routine at the frequency of interest. All steady-state measurements used the same acquisition parameters. A 5 second record was acquired at a sampling frequency of 51.2 khz. The record was divided into 1 averages, a Hanning window was applied to each average, and spectral processing resulted in a frequency resolution of.78 Hz. In the transient case, time records were acquired at 12.4 khz and filtered at the frequency of interest, in order to remove other components from the response. The filtered signal was then enveloped using a Hilbert transform, and amplitudes of the first group arrival waveform were extracted for each gage. These amplitudes were then run through the PSL calculation, using Equations Figure 2.3: Principal strain localization processing algorithm for both transient (red) and steady state (blue) single tone excitations. Note that repeated estimates may be calculated from multiple rosettes, frequency components, and additional averaging. 3

51 2.3 Initial Acoustic Source Testing An initial performance test of the PSL method aimed to detect a vibration source mounted on the plate structure, using the developed processing techniques. For this test, the stiffener was removed, and the high frequency shaker was mounted at various bolt hole locations, as shown in Figure 2.4. Strain measurements were acquired only for Rosettes 1 and 3. For the steady-state drive, a frequency of 2 khz was chosen (corresponding to a bending wavelength of 11.1 cm) and a high voltage input was used in order to assure high signal-to-noise measurements from the mounted strain sensors. Sensor rosettes were located between 25 cm and 41 cm from the source, depending on the position of the shaker. This resulted in a propagation of at least 2 full wavelengths of the drive frequency before reaching the receivers. Force amplitudes at 2 khz were measured to be.7 N in magnitude. After acquiring a steady-state signal, the drive amplitude settings were kept approximately constant and a transient tone burst signal was acquired. The tone burst consisted of a 5-cycle Hanning windowed sine wave at the drive frequency. Figure 2.4: Acoustic source localization testing setup. The high frequency F7 shaker was mounted directly to the unstiffened plate, at various bolt hole positions. A progression of PSL localization tests was performed using steady-state and transient signals. 31

52 The acoustic source test provided some initial insight into the PSL technique, and its application to steady-state and transient signals. Figure 2.5 shows resulting amplitude spectra for each gage in Rosette 1, with peak strain levels indicated at the drive frequency. The 1, 2 and 3-direction gages measured.49 µ-s,.42 µ-s, and.54 µ-s, respectively. Similar measurements were made for the transient tone burst excitation. Figure 2.6 shows the acquired time signal, the third octave filtered signal at the drive frequency, and the enveloped signal used to extract strain amplitudes. The first group arrival waveform was identified and the peak of the envelope was found using the gage with the highest signal-to-noise response (gage 1). Since the propagating wave passes through each gage in the rosette at approximately the same time, strain amplitudes were extracted from the other gages in the rosette at the same time step. The 1, 2 and 3-direction strain amplitudes were measured as.8 µ-s,.51 µ-s, and.42 µ-s, respectively. These transient strain amplitudes were also run through the PSL algorithm. Comparing the transient and steady-state excitations at the center position of the plate, with the same peak drive amplitude, the signal-to-noise is demonstrated to be much higher in the steady-state condition. For instance, the peak strain level measured by the first gage in rosette 1 is nearly an order of magnitude higher for the steady-state excitation (.49 µ-s versus.8 µ-s in the transient case first group arrival). The higher signal-to-noise, however, does not necessarily result in more accurate angle estimates. Figure 2.7 shows the resulting calculated PSL angles, illustrated on vector plots (viewed from the opposite side of the plate shown in Figure 2.1, where the shaker, stiffener and gages are attached), for various source locations. Data from each of the other locations can be found in Appendix A.1. Both steady-state and transient methods provide satisfactory results for many of the tested source locations. The angle estimates vary in accuracy, with the transient case showing typically higher quality estimates. Both methods show accurate estimates at positions 1, 2, 4, and 5, while the transient method tends to be more accurate for positions 3 and 6. A major factor affecting these estimates is the level of reflection from the boundaries of the plate structure. Because the steady-state excitation includes the superposition of direct and reflected waves, these estimates may vary greatly depending on the position of the source with respect to the receiving rosettes. In the transient case, reflections from the boundaries are excluded from the angle estimate because of the specific selection of the first group arrival waveform. However, 32

53 the low signal-to-noise may affect the quality of the strain amplitude measurements. Since the virtual source of the damage is inherently of a lower signal strength compared to a driven source, accurate damage location estimates were difficult to obtain with a transient excitation. These results are discussed in detail in Chapter 3. 33

54 1 Amplitude Spectrum of Strain 1 1 Strain (µ S) µ S Frequency (khz) 1 Amplitude Spectrum of Strain 1 2 Strain (µ S) µ S Frequency (khz) 1 Amplitude Spectrum of Strain 1 3 Strain(µ S) µ S Frequency (khz) Figure 2.5: Strain amplitude spectra for each gage in Rosette 1, using a steady-state excitation of 2 khz at the center position on the plate. These strain amplitudes were extracted and used to localize the source using the PSL processing method outlined in Section

55 Amplitude (µ S) Strain 1 Time Record (DC Offset Removed) Gage 1 Gage 2 Gage Time (s) Strain 1 Filtered Time Record Amplitude (µ S).1.1 Amplitude (µ S) Time (s) Strain 1 Filtered Enveloped Time Record First Group Arrival Time (s) Figure 2.6: Strain measurements for each gage in Rosette 1, using a tone burst excitation of 2 khz at the center position on the plate. The time signal was filtered and enveloped. Strain amplitudes were chosen from the first group arrival in the enveloped waveform. 35

56 Localization Plot (Steady state Method) Localization Plot (Transient Method) Y Position (cm) Y Position (cm) X Position (cm) (a) Center position 1, steady-state result 6 5 Localization Plot (Steady state Method) X Position (cm) (b) Center position 1, transient result 6 5 Localization Plot (Transient Method) Y Position (cm) Y Position (cm) X Position (cm) (c) Position 2, steady-state result X Position (cm) (d) Position 2, transient result Localization Plot (Steady state Method) Localization Plot (Transient Method) Y Position (cm) Y Position (cm) X Position (cm) (e) Position 4, steady-state result X Position (cm) (f) Position 4, transient result Figure 2.7: PSL position estimates for various source positions (shown in green) on the aluminum plate. A 2 Hz drive frequency was used, with a bending wavelength of 11.1 cm. This resulted in approximately 2 4 propagation wavelengths between the source and receivers. 36

57 2.4 Modulated Wave Data Processing and Automation Techniques The modulated wave method required a more rigorous processing scheme for damage detection and localization studies. Where a single tone steady-state drive requires careful selection of drive frequencies to excite a high nonlinear response, the modulated wave method typically shows high nonlinear content over a range of frequencies, and information about the damage is contained in a number of sideband components around the high drive frequency. Once time records were acquired in the damaged condition, PSL processing followed the routine outlined in Figure 2.8. Each steadystate strain signal was converted to the frequency domain, and amplitudes were extracted from the first 4 positive and negative sidebands in the response (f±, 2f±, 3f± and 4f±), around the high drive frequency. Because of the varying signal-tonoise of the individual sideband components, a sifting routine was implemented to automate removal of low signal-to-noise components. A 1 db threshold was used with a noise floor reference to remove those components with low level amplitudes. The remaining sideband amplitudes were then summed up for each gage in a rosette, and these total nonlinear amplitudes (A ε1, A ε2, and A ε3 ) were then passed through the principal strain angle calculation. The angle estimates from the 3 strain rosettes were used to provide an estimate of the damage location. Implicit in this processing scheme is the need for additional averaging and additional drive conditions to improve the confidence of individual localization estimates. The steady-state modulated wave method was used in developing an algorithm for automation of the nonlinear vibration based method, suitable for embedded airframe applications. This process was systematically carried out on each test bed to evaluate drive frequencies, amplitudes, and repeatability of damage localization estimates. The complete algorithm is shown in Figure 2.9. The process begins with an initial selection of drive frequencies based on the damage size of interest. In general, nonlinear vibration based metrics have been shown to be effective when driving at frequencies with wavelengths on the order of the damage size. Wave dispersion relations can be used to set an approximate range of drive frequencies for the active interrogation of the structure. Note that in the frequency ranges used throughout this study, only A (bending wave) modes were excited, though other, 37

58 Figure 2.8: Principal strain localization algorithm for a steady-state modulated wave excitation. Nonlinear sideband amplitudes are extracted, low-level sidebands (<1 db signalto-noise in this study) are sifted out of the routine, and high signal-to-noise components are summed for each sensor in a rosette. These total nonlinear contributions are then run through the PSL routine to estimate the damage location. higher order modes may be utilized depending on the damage of interest. Once a range of high and low excitation frequencies is identified, a database of healthy wave modulation data is established. This step is necessary because all materials and most structures contain some inherent nonlinearity. When damage is introduced into the system, this level of nonlinearity increases. Therefore over time, as damage occurs, subsequent scans can be performed and damaged modulated wave data can be compared to the healthy baseline. Sideband components are easily tracked for each drive condition using a ratio of damaged and healthy sideband amplitudes. The conditions showing the highest increase in nonlinear content are chosen for further study. Using the PSL processing scheme for a modulated wave excitation (shown in Figure 2.8), angle estimates are obtained at varying high and low frequency forcing levels in order to observe the sensitivity of the localization results to drive amplitude. Once a consistent estimate is found, measurements are repeated to increase confidence in the localization estimate. 38

59 A limited range of drive frequencies were studied throughout this work, in order to simplify the algorithm for manual use in the laboratory environment. However, the algorithm shows high potential for a truly automated system, which can scan through a wide range of drive conditions to seek out peak nonlinear responses. A healthy database can be established for a range of drive conditions, environmental conditions, and varied static and dynamic loading. Damage location summaries can be collated over time, and further statistical processing can be employed to enhance the reliability of the detection system. This sophisticated automation is an important topic for future study. Figure 2.9: Proposed algorithm for nonlinear modulated wave localization and automation. A direct comparison between healthy and damaged conditions is used to select drive frequencies. Further processes are used to evaluate drive levels necessary for accurate localization. This process was carried out systematically for different test beds and damage conditions. 2.5 Damping Effects One factor affecting the application of the PSL approach is the level of damping in the structure. Because the modulated wave localization approach is a steadystate vibration phenomenon, an important aspect of the localization capability may 39

60 be the reverberation radius, and the distance traveled by the propagating bending wave between the damage and sensors. The effect is analogous to the 3-dimensional reverberation radius in room acoustics. For the 2-dimensional plate test bed, higher damping results in less reflections from the boundaries, and more direct field vibration from the source (or damage) passing through the strain rosette locations. Less damping results in increased reflections from the boundaries, which can potentially contaminate the direct strain waves traveling from the damage location Reverberation Radius A formulation developed by Davis [51] uses power balance principles to write an expression for the reverberation radius in plate structures. At the basis of the formulation is the idea that for a steady-state excitation, the ratio of the velocity at a receiver, v R, to the drive point velocity, v S, is inversely proportional to the distance d from the source, by the expression [52]: v 2 R(d) v 2 S = 2 πk B d. (2.1) In this expression, k B is the bending wavenumber corresponding to the excitation frequency from the source, and the reduction in velocity amplitude from the source to the receiver is a result of the presence of damping in the system. Using power balance principles, the input power P S from the source can be equated to the transmitted power at the receiver location P R, P S = P R, (2.2) where the input power due to a steady-state forcing function is typically expressed as P S = 1 2 Re[ F S v S ]. (2.3) In this input power expression, FS represents the complex forcing at the source location, and again Re is used to designate the real part of the complex quantity. Equation 2.3 can be written in terms of the drive point impedance Z S. The drive 4

61 point impedance is defined as Z S = F S v S = 8ωm, (2.4) kb 2 where ω is the excitation frequency and m is the plate surface mass density (mass m per unit area A of the plate). Combining Equations 2.3 and 2.4, the input power can be written as P S = 1 2 v2 S Re[ Z] = v 2 S 4ωm k 2 B = v S 2 4ωm. (2.5) AkB 2 The transmitted power at the receiver location can then be written using statistical energy analysis principles, P R = 1 2 m v2 Rωη, (2.6) where η is the damping loss factor for the plate. Equating 2.5 and 2.6, the mass and frequency terms cancel. Rearranging the remaining terms, the ratio of the received velocity to the drive point velocity can be written: v 2 R v 2 S = 8. (2.7) ηakb 2 Combining Equations 2.1 and 2.7, the reverberation distance can finally be written: d reverb = ηak B 4π. (2.8) From this expression, the reverberation radius in a plate structure is shown to depend on the damping in the system, and the wavenumber of the propagating bending wave. Therefore, it is also dependent on the frequency of excitation, and its corresponding bending wavelength. Since the direct field contains the most information about the direction of the acoustic waves from the source, it would be plausible for the PSL estimate to be most accurate when the strain rosette lies within the reverberation radius. Therefore, structural damping was one of the parameters explored in evaluating the damage localization approach on the stiffened plate test bed. 41

62 2.5.2 Damped Stiffened Plate Initial damage detection and localization studies were performed on the unmodified stiffened aluminum plate structure. To evaluate the effects of damping on the localization technique, edge damping treatment was added to the plate, as shown in Figure 2.1. As an added benefit, the damping material would also decrease any nonlinear effects stemming from the boundaries of the plate, such as contact nonlinearities between the aluminum plate and steel frame. Soundcoat 66 viscoelastomer (1.3 mm thick) was cut into 1.5 cm wide strips and used to line the edges on both sides of the plate. Figure 2.1: Soundcoat 66 edge damping treatment (1.5 cm wide x 1.3 mm thick) used on the stiffened aluminum plate test bed Loss Factor Measurements To evaluate the effects of the added damping treatment on the plate test bed, a high frequency accelerometer (PCB Piezotronics model 621B4) was installed at each rosette location and the F7 shaker was used to excite a white noise signal in the bandwidth of 1 2 khz. The steady-state signal was turned off to capture reverberation time measurements in a healthy plate condition, as well as a fully damaged (3 rows loose) condition. Data was obtained for both undamped and damped 42

63 plate configurations. Time records from the three accelerometer measurements were filtered at one third octave (OTO) band frequencies between 1 khz and 2 khz, enveloped using a Hilbert transform, averaged over the three measurement locations, and used to calculate decay rates for each octave band center frequency. The results for the healthy plate are shown in Figure 2.11, while results for the damaged plate are shown in Figure Figure 2.13 shows the ratios of loss factors in the damped (η d ) and undamped (η) plate configuration, for both healthy and damaged conditions. In general, loss factors are shown to increase across the entirety of the bandwidth for the healthy plate condition, from undamped to damped plate configurations. In addition, the damaged plate exhibits higher loss factors compared to the healthy plate in the range of 1 4 khz. This is likely due to acoustic and friction losses from the loose stiffener. Note that linear techniques mentioned in Chapter 1 often use damping changes as damage indicators. However, the approach generally shows low sensitivity, poor repeatability, and high sensitivity to environmental conditions [3, 4]. 1 1 Damping Measurements for Healthy Plate Undamped Damped Loss Factor Frequency (Hz) Figure 2.11: Healthy OTO band loss factor measurements on the stiffened aluminum panel from 1 khz to 2 khz. Edge damping treatment is shown to increase loss factors in all frequency bands. 43

64 1 1 Damping Measurements for Damaged Plate Undamped Damped Loss Factor Frequency (Hz) Figure 2.12: Damaged (3 fastener rows loose) OTO band loss factor measurements on the stiffened aluminum panel. Loss factors are shown to increase in the bands above 63 Hz. Studying the net increase in loss factors for both healthy and damaged plate conditions, the damaged plate shows net increases in loss factors above the 63 Hz center frequency, but shows some low level increases and decreases in the range of 63 Hz and below. These results are inconsistent with those found in the healthy condition, and can be attributed to nonlinear damping effects in the presence of the stiffener damage. The nonlinear behavior of the stiffener may cause increased radiation and friction losses in the undamped plate configuration, where these effects are lessened in the damped plate configuration, causing lower loss factors at certain frequency bands. The third octave band showing the highest loss factor is at 5 khz, in all tested conditions. In the healthy condition, the measured loss factor is.128 in the damped configuration, and.12 in the undamped configuration. In the damaged configuration these values are measured as.16 and.169 in damped and undamped configurations, respectively. The treatment has little effect at this frequency band, suggesting that damping effects from the damage are contributing to the high loss 44

65 3.5 3 Healthy Damaged Damping Increase Factors 2.5 η d /η Frequency (Hz) Figure 2.13: Damping increase factors for both healthy and damaged conditions on the stiffened aluminum panel. Damping is shown to increase at each center frequency in the healthy condition, while the damaged condition shows both increased and decreased damping in the frequencies below 63 Hz. This could be due to nonlinear damping effects from the damaged joint condition. factors. Plotting bending wavelength dispersion curves and comparing to acoustic wavelengths in air, the critical frequency of the aluminum plate is shown at 48 Hz. Figure 2.14 shows this relation, using plate bending wave expressions from Fahy and Gardonio [53]. At the critical frequency, the plate radiates sound most efficiently, meaning that most losses in the frequency band near 5 khz are from sound radiation. Since the structural damping for the plate is relatively low overall (.1), this explains why the highest damping appears at the critical frequency. For damage detection and localization, damping levels had an impact on effective excitation frequencies and amplitudes, used for interrogation of the damaged joint conditions in both damped and undamped plate configurations. Using Equation 2.8 with measured loss factors and calculated wave numbers for the stiffened plate, reverberation radius estimates for the damaged condition were determined, as shown in Figure The largest reverberation distance corresponds to the highest damping, 45

66 1 4 Aluminum Plate Wavelengths c Beff Wavelength (cm) c L c S c air Frequency (Hz) Figure 2.14: Wavelengths for bending, longitudinal, and shear waves traveling in a.25 cm thickness aluminum plate, similar to the stiffened aluminum plate test bed. The critical frequency of the plate is shown at 48 Hz. in the 5 khz band. As damage was interrogated and localized throughout this study, effective excitation frequencies were compared with these damping and reverberation radius estimates, to assess any effects on the localization capability. Note that the typical distance from the damage condition to the sensor rosette was approximately 2 4 cm, depending on the damage position. As shown in Figure 2.16, this was always greater than the maximum predicted reverberation radius ( 6.5 cm). However, mounting sensors in such a close proximity to the damage would be unrealistic in most cases. It was hypothesized that the most accurate damage localization would be achieved by localizing on nonlinear content in ranges of the bandwidth where the reverberation radius was largest. Driving with an active excitation near high damping regions would be necessary to satisfy this condition. Chapters 3 and 4 provide detailed discussion on damage localization results using both undamped and damped stiffened plate configurations. 46

67 Reverberation Radius (cm) Reverberation Radius Estimates Undamped Damped Frequency (Hz) Figure 2.15: Calculated reverberation radius for the damaged plate condition, in both damped and undamped plate configurations. The largest reverberation distance corresponds to the point of highest structural damping. Figure 2.16: Sketch of approximate reverberation radius (in red) for the 3 rows loose damage condition. Typical distances from the damage to each sensor rosette are shown. Throughout localization testing, all sensors were mounted at distances greater than the maximum reverberation radius of 7 cm. 47

68 2.6 Nonlinear Regime Measurements While damping and general signal-to-noise issues can affect the ability to detect and localize on damage using acquired strain responses, another primary factor is the characteristic of the nonlinear response. The state of the nonlinear response can change drastically as drive amplitude increases, transitioning from regions of orderly higher harmonics, to regions of unstable local resonances and eventually broadband chaos. This phenomenon was discussed in detail in Chapter 1, and illustrated in Figure 1.6. As testing progressed, these nonlinear regimes had a significant impact on the ability to localize on the damage when driving at high forcing conditions. An illustrative study was conducted to view the onset and transition of nonlinear regimes using the damped stiffened plate configuration and 3 rows loose damage condition. A frequency scanning method was employed to find a single tone drive frequency causing a high nonlinear response of the damage. Guided by previous studies [44, 46], an excitation frequency of 22 Hz was chosen. 5 different forcing amplitudes were run on both the healthy and damaged (3 fastener rows loose) plate conditions:.1 N,.26 N,.43 N,.76 N and 1.11 N. Strain amplitude spectra from the 1-direction gage in rosette 1 were plotted to observe the nature of the nonlinear response. Results from all forcing conditions are shown in Figures 2.17 and 2.18, showing a gradual increase in nonlinear content with increasing drive amplitude. Studying the responses, results are consistent with the coupled nonlinear oscillator model shown in Figure 1.6, as well as the bilinear stiffness model shown in Table 1.3. The strain response begins with low level nonlinear content at a force amplitude of.1 N. The 2f harmonic is present, as well as traces of subharmonics and ultrasubharmonics (f/2, 3f/2, 5f/2, and 7f/2) in the damaged condition. At.26 N of forcing, the f/2 component shows a large increase in amplitude, while other higher harmonic components begin to appear in the response. Further nonlinear content appears at a drive amplitude of.43 N, with prominent f/2 and 3f/2 components. Traces of 5f/2 and 7f/2 components also appear at this higher drive level. More higher harmonics appear in the response, with amplitude dependencies matching the sinc-envelope pattern (Table 1.3) shown by Solodov [23]. As drive amplitude continues to increase, the damaged response transitions to a chaotic state (Figure 2.18). Subharmonic content is still visible in the.76 N drive condition, but these components are obscured by the broadband chaotic response in 48

69 the 1.1 N forcing case. When tracking information from discrete nonlinear frequency components, the chaotic response can prevent an automated method from extracting valuable strain amplitudes at the frequencies of interest. Note that at higher drive levels, the healthy response begins to show higher order nonlinear content, similar to that shown in the damaged condition at lower drive levels. In the 1.1 N forcing case, traces of the f/2 and 3f/2 components begin to appear in the healthy response. Figure 2.19 focuses on the narrow band around the drive frequency, for the.43 N and 1.1 N drive conditions. The damaged response shows ultra-frequency pair content in the.43 N case, before transitioning to chaos in the 1.1 N case. Meanwhile, the healthy response shows low nonlinear content in the low forcing case, and ultra-frequency pairs in the high forcing case. The progression suggests that, while subharmonics and ultra-subharmonics only appear at high levels in the damaged condition, the healthy condition is susceptible to other forms of nonlinearity, which may be an inherent nonlinear effect of the material and fastened stiffener, or a nonlinear effect of the active drive system. 49

70 Magnitude (db re 1 µ S) Magnitude (db re 1 µ S) f/2 f drive 2f 3f/2 Damaged Healthy Frequency (khz) f/2 f drive 3f/2 2f (a).1 N force amplitude 3f Frequency (khz) Magnitude (db re 1 µ S) f/2 f drive 3f/2 2f (b).26 N force amplitude 3f 5f/2 7f/ Frequency (khz) (c).43 N force amplitude Figure 2.17: Strain response showing a progression from orderly higher harmonic content to unstable subharmonic and ultra-subharmonic response. Low levels of nonlinearity are shown in the healthy response. 5

71 Magnitude (db re 1 µ S) Magnitude (db re 1 µ S) Subharmonics and chaotic response Damaged Healthy Frequency (khz) (a).76 N force amplitude Broadband chaotic response Frequency (khz) (b) 1.1 N force amplitude Figure 2.18: Strain response at higher drive levels, exhibiting growth of the broadband chaotic response. The healthy condition begins to show signs of ultra-frequency pairs around the drive frequency and higher harmonics. 51

72 Magnitude (db re 1 µ S) Magnitude (db re 1 µ S) Ultra frequency pairs Damaged Healthy Frequency (khz) (a).43 N force amplitude (zoomed at 22 Hz drive) Damaged Healthy Frequency (khz) (b) 1.1 N force amplitude (zoomed at 22 Hz drive) Figure 2.19: Narrowband view of 22 Hz drive in.43 N and 1.1 N forcing conditions. The damaged response shows ultra-frequency pair content at lower force amplitudes. The healthy condition also shows ultra-frequency pairs, but at higher forcing levels where the damaged condition has already transitioned to chaos. 52

73 2.7 Method Summary and Approach With data processing methods developed for both modulated wave and single tone excitations, and an understanding of various factors influencing localization capability, the undamped stiffened plate configuration was used for initial damage detection and localization studies. Single tone and modulated wave nonlinear methods were explored and compared. Particular emphasis was placed on developing the modulated wave method for automation procedures in embedded systems, as outlined previously in Figure 2.9. Once damage conditions were evaluated, damping treatment was added and similar conditions were repeated for the damped plate configuration. Damping effects were assessed, in preparation for transitioning the localization scheme to a real airframe test bed. Once techniques were fully developed on the stiffened plate, simulated damage conditions were induced on a UH-6A upper cabin structure, in order to apply the detection scheme to a more realistic airframe application. 53

74 Chapter 3 Undamped Stiffened Plate Results 3.1 Single-tone Damage Detection Results Previous research in nonlinear detection methods has shown the signal-to-noise benefits of a steady-state excitation, while in guided wave methods localization is typically performed using a transient tone burst signal and time of flight measurements. The first damage detection study used the undamped plate configuration (described in Section 2.1) and the largest damage increment (3 fastener rows loose) to test localization capability with both steady-state and transient excitations. The 3 rows loose damage condition created approximately a 15 cm x 2.5 cm unfastened gap in the plate/stiffener joint, shown in Figure 3.1. This damage is representative of degraded joint damage on typical airframe structures, involving working rivets and loss of torque in fasteners. The transient method used in this study attempted to utilize the PSL approach, by focusing on the time dependent nonlinear strain components generated by a transient tone burst traveling through the damaged joint location Steady-state Localization Results The study began by using a steady-state excitation and frequency scanning method to find a condition showing a high nonlinear response, in the form of subharmonics and ultra-subharmonics of the drive frequency. Previous studies [44, 46] on the undamped plate setup aided in the initial selection of frequencies. In addition, transfer functions between the strain and force measurements were used to show frequency ranges with 54

75 Figure 3.1: Largest damage increment, with 3 fastener rows loose. This created approximately a 15 cm x 2.5 cm gap in the plate/stiffener interface.. high strain response for a given force input. A condition with high transmissibility and a high nonlinear response was found at 2227 Hz, with -8 db (.16 N) of force amplitude. The corresponding strain response for each gage in rosette 1 is shown in Figure 3.2, for both damaged and healthy plate conditions. This force level was considered low enough, that small, lightweight actuators could be used to provide adequate forcing at the required drive frequency (such as commercially available piezoelectric actuators, with masses on the order of 1 1 g). As expected, the strain response spectra in the damaged condition exhibit high amplitude subharmonics and ultra-subharmonics of the drive frequency. Higher harmonics are present in both damaged and healthy conditions, but the damaged response shows considerable ultra-frequency pair content around the drive frequency and harmonics. These higher order nonlinear effects could potentially be reduced by using lower drive force levels. However, the single-tone nonlinear response is highly sensitive to changes in frequency and amplitude. As a result, drive amplitude changes were not explored for this condition. Instead the single tone PSL processing scheme (detailed in Figure 2.3) was used at this drive condition alone to provide an estimate of the damage location. Individual subharmonic responses were targeted at f/2, 3f/2, 5f/2, and 7f/2. For comparison, a total nonlinear estimate was also made, similar 55

76 Magnitude (db re 1 µ S) f/2 f drive 3f/2 5f/2 Amplitude Spectrum of Strain 1 1 Damaged Healthy Frequency (khz) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Figure 3.2: Damaged versus healthy strain responses for rosette 1, under a single tone excitation at 2227 Hz, -8 db. The damaged response shows high subharmonic and ultrasubharmonic responses, as well as ultra-frequency pairs around the drive frequency and higher harmonics. 56

77 to that outlined in the modulated wave localization processing (Figure 2.8). Rather than summing up contributions from the sideband components, the subharmonic contributions were added up in an effort to take more of the nonlinear response into account in the localization scheme. Figure 3.3 shows the localization estimates for each processing method. The nonlinear component with the highest signal-tonoise, f/2, shows one of the most accurate estimates, with approximately 26 angle estimates shown for both rosette 1 and 3. Because of the lower magnitude of the other components, f/2 tends to dominate the total nonlinear estimate. Note that this view of the plate is from the side where the shaker and sensors were mounted. Rosette 2 (lower right) shows poor estimates in all conditions, where rosettes 1 (upper right) and 3 (lower left) show accurate estimates for f/2 and 7f/2. Note that the location of rosette 2 was later varied in an effort to improve the signal in this location (the final position was that shown in Figure 2.1). A primary concern with the steady-state single-tone approach is the lack of control over the amplitude of the nonlinear signature from the damage. Since the single tone CAN effect is due to a parametric resonance, it is inherently unstable and requires judicious selection of drive frequency and amplitude. It can often be difficult to obtain high signal-to-noise nonlinear signatures using a single-tone approach alone. As a result, use of the PSL method can be problematic when focusing on the unstable nonlinearities of a single-tone excitation. A key benefit of the more stable modulated wave approach is the selection of drive frequencies and amplitudes to effectively control the amplitude of nonlinear signatures from the damage. Detailed discussion of modulated wave results can be found in Section

78 Localization Plot (Steady state Method) Localization Plot (Steady state Method) Y Position (cm) Y Position (cm) X Position (cm) X Position (cm) (a) f/2 (b) 3f/2 Localization Plot (Steady state Method) Localization Plot (Steady state Method) Y Position (cm) Y Position (cm) X Position (cm) (c) 5f/2 6 5 Localization Plot (Steady state Method) X Position (cm) (d) 7f/2 Y Position (cm) X Position (cm) (e) Total Nonlinear Figure 3.3: Single tone, steady-state damage localization estimates performed using each nonlinear component individually, as well as a total nonlinear estimate. The source position is shown in green, while the damage size and location is shown in red. 58

79 3.1.2 Transient Localization Results With the 2227 Hz drive condition chosen in Section 3.1, a 5-cycle tone burst was driven at the same frequency in an effort to excite a transient nonlinear scattering effect at the damage location. The transient processing algorithm shown in Figure 2.3 was used to extract PSL estimates from the acquired strain time records. Since it was assumed a higher transient force level would be needed to excite the nonlinear response, the signal gain was increased over that used in the steady-state case. A peak force level of 1.8 db (1.5 N) was used for the tone burst excitation, shown in Figure 3.4. Note this force level is still considered low for an embedded application. Responses were studied for each strain rosette, with signals OTO filtered at the f/2, 3f/2, and 5f/2 nonlinear components. Figure 3.5 shows the resulting strain time record, the f/2 filtered record, and the enveloped signal for rosette 3. The first group arrival of the nonlinear component is shown near.5 s, with gage 2 showing a maximum strain amplitude of.25 µ-s. Taking the strain magnitude for each gage at the same time step, where the peak occurs in the group arrival waveform, a PSL estimate was calculated using the time record. By comparing with the acquired f/2 strain amplitude in the steady-state condition, the low signal-to-noise of the transient response becomes evident. The f/2 component strain amplitude for rosette 3, gage 2, in the steady-state condition, is.15 for.16 N of force amplitude. Nearly an order of magnitude greater peak force in the transient case increases the peak strain response by a factor of 1.6 over the steady-state case. As shown in Figure 3.6, the resulting PSL angle estimate for f/2 is comparable, while 3f/2 remains inaccurate. 5f/2 yields a more accurate result in the transient case. Acquired and processed time data for rosette 3, filtered at 3f/2 and 5f/2, are located in Appendix A. 59

80 Amplitude (N) Impedance Head Force Record Drive Reflections Time (s) Figure 3.4: Transient tone burst force signal at 2227 Hz, with amplitude of 1.5 N. After the initial 5-cycle pulse, reflections from the boundaries appear in the impedance head response. A number of factors can influence detection capability using a transient excitation. First and foremost is the ability to drive the nonlinear response with enough energy. The Wilcoxon F7 shaker is sufficient to drive high amplitude signals, and the force measurement from the impedance head suggests that the shaker has the ability to excite a strong tone burst signal. However, a short burst may not provide enough energy at the damaged interface to excite a strong CAN effect. This could explain the poor estimates when focusing on certain nonlinear components (such as 3f/2), where the signal-to-noise of the propagating nonlinear component is very low. The transient method is also difficult to implement in an automated routine. At high frequencies, where the wave speeds are higher, reflections from the boundaries have a tendency to bleed into the initial waveform. Depending on the length of the burst used, and the distance to the boundaries of the interrogated structure, selection of the first arrival waveform can be problematic. Furthermore, over increasing distance, the transient method is subject to the same dispersion issues seen in guided wave methods. Amplitudes of the source waveform and damaged signature waveform decrease rapidly over the distance to the receiver. As a result, the quality of the angle estimate is highly dependent on this distance. This could indicate why the furthest receiver, rosette 2, continually shows poor angle estimates. 6

81 Amplitude (µ S) Strain 3 Time Record (DC Offset Removed) Gage 1 Gage 2 Gage Time (s) 4 x 1 3 Strain 3 Filtered Time Record Amplitude (µ S) Time (s) Amplitude (µ S) 4 x 1 3 Strain 3 Filtered Enveloped Time Record First Nonlinear Group Arrival Time (s) Figure 3.5: Transient response for rosette 3, filtered at the f/2 subharmonic. The first group arrival of the nonlinear component is near the.5 s. Gage 2 shows a peak amplitude of.25 µ-s. 61

82 Localization Plot (Transient Method) Localization Plot (Transient Method) Y Position (cm) Y Position (cm) X Position (cm) (a) f/2 6 5 Localization Plot (Transient Method) X Position (cm) (b) 3f/2 Y Position (cm) X Position (cm) (c) 5f/2 Figure 3.6: Transient PSL angle estimates, focusing on nonlinear subharmonics and ultra-subharmonics of 2227 Hz. The f/2 estimate is comparable to that in the steady-state case. 62

83 3.2 Modulated Wave Damage Detection Results Based on its high potential for automated damage detection, the modulated wave method was developed on the stiffened plate structure. Using the processing scheme outlined in Figure 2.8, and the automation approach shown in Figure 2.9, the modulated wave PSL approach was first evaluated on the undamped plate configuration, with the 3 rows loose damage increment. Once evaluated on the largest damage size, the approach was repeated using the 1 row loose damage condition, a condition representative of early initiation of working rivets and loss of fastener torque. The 1 row loose condition corresponded to an approximate 5 cm x 2.5 cm damage footprint. The tested damage sizes and positions on the joint are illustrated in Figure 3.7. Figure 3.7: Tested damage conditions on the undamped stiffened plate, using a modulated wave excitation. In addition to the 3 rows loose damage size, a 1 row loose condition was assessed. In following the automation process, a set of drive frequencies was first chosen. Based on the bending wave dispersion curves for the plate test bed (Figure 2.14), a 75 Hz low drive (exercising wave) frequency was determined to have a corresponding wavelength similar in size to the long dimension of the of the 3 rows loose damage increment. A high frequency (probing wave) range of 4 khz to 9 khz was chosen for initial healthy condition surveys, allowing ample room for evenly spaced 75 Hz sidebands in the acquisition bandwidth above and below the high drive frequency. 63

84 Note that the 75 Hz active low drive was held constant throughout much of the modulated wave testing, in order to reduce the number of variables in the evaluation of the automation algorithm. Since the purpose of the low frequency excitation is to modally excite the damaged interface, it is assumed that as long as the low frequency provides enough forcing, it should be effective for other damage sizes. For a truly automated system, a range of low frequencies may be tested along with a range of high frequencies to build up a more detailed database of healthy baselines. In addition, each frequency pair could be assessed in varying operational and environmental conditions to expand the range of baseline data for comparison. For complex geometries, precise bending wave dispersion relations are difficult to calculate, posing potential difficulties in evaluating the starting and ending points for drive frequency ranges and wavelengths corresponding to the damage size of interest. While accurate numerical simulation of wave dispersion relations could aid in the frequency selection process, only approximate wavelengths are necessary, if the range of tested frequencies covers a wide enough band to interrogate a wide range of damage sizes. The comparison with the healthy baseline then assures that detected nonlinear signatures are indicative of damage in the system. Force amplitudes for both high and low frequency drives were recorded using the impedance head at the collocated shaker drive point. Initially, -8.2 db (.15 N) of force was supplied to the low frequency shaker, while -3.6 db (.44 N) was supplied through the high frequency shaker. These amplitude levels were held approximately constant as high frequencies were individually scanned from 4 khz to 9 khz in 5 Hz increments. The 75 Hz low drive frequency was held constant for each data point. The time records were recorded and stored for later use, representing the healthy database component of the automation process. In an airframe application, later surveys would be made over time, during operation, and an automated system could choose interrogation frequencies based on the net increase of nonlinear components for a given drive condition. These frequencies would then be used for further evaluation. This process was carried out on the plate test bed, by inducing damage and running the same scan of drive conditions. 64

85 Rows Loose Damage Condition The largest damage condition was induced first, by loosening the 3 rows of fasteners on the plate/stiffener joint. The range of drive conditions was repeated for the damaged condition and the damaged data sets were compared directly to their healthy counterparts. Amplitudes for the first 4 positive and negative sidebands (f ±, 2f±, 3f± and 4f±) were extracted from the healthy and damaged condition strain spectra, for each drive condition, and for each gage on the structure. Corresponding damaged and healthy sideband amplitudes were divided (A D /A H ) in order to observe the drive conditions showing the highest increase in nonlinear response, a direct effect of introducing damage into the structure. Figure 3.8 shows the amplitude ratios for each gage in rosette 1. A number of sideband components show a significant increase in amplitude from healthy to damaged conditions, likely due to the large size and high nonlinearity of the 3 rows loose damage footprint. A number of drive conditions could be chosen for further study, based on the high increase in nonlinear components in the range of 4 Hz to 6 Hz. For instance, the f1 component at 45 Hz (gage 1), f2 at 5 Hz (gage 2), and f4 at 6 Hz (gage 2) all show 15 db increases from healthy to damaged conditions. The 6 Hz condition was chosen for further study, because the higher order nonlinear component (f 4 ) typically is indicative of a high level of nonlinearity in the structure. Figure 3.9 shows the damaged and healthy strain spectra at the 6 Hz drive condition. As illustrated in the amplitude ratios, the minus sideband components show significant increases from healthy to damaged conditions. The primary example is the f4 component in gage 2, where a 15 db increase occurs in the presence of damage. Note also that higher harmonics show significant increases in amplitude, though this varies across the gages. Careful observation of the spectra shows that the third harmonic of the drive frequency is in fact at the same frequency as the f4 sideband component. If the third harmonic is primarily a function of the damage, and not harmonic distortion of the active drive system, the interaction of these two nonlinear signatures may actually be a benefit to the detection approach. This could also explain why the nf sidebands show much higher amplitudes in the strain response than the nf + components. 65

86 A D /A H (db re 1 µ S/µ S) Strain 1 1 Sideband Amplitude Ratio High Frequency (Hz) A D /A H (db re 1 µ S/µ S) Strain 1 2 Sideband Amplitude Ratio High Frequency (Hz) f1 f2 f3 f4 f1+ f2+ f3+ f4+ A D /A H (db re 1 µ S/µ S) Strain 1 3 Sideband Amplitude Ratio High Frequency (Hz) Figure 3.8: Damaged versus healthy sideband amplitude ratios for the 3 rows loose damage condition, in the undamped plate configuration. A peak condition is shown at 6 khz, where the 4f sideband component (gage 2) shows a 15 db increase from healthy to damaged conditions. This drive frequency was chosen for further examination. 66

87 Magnitude (db re 1 µ S) f low Amplitude Spectrum of Strain 1 1 f4 f3 f Frequency (khz) f1 f high f1+ f2+ Damaged Healthy Magnitude (db re 1 µ S) Amplitude Spectrum of Strain 1 2 f4 +15 db Frequency (khz) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Figure 3.9: Damaged versus healthy strain spectra for each gage in rosette 1, using a 6 khz high frequency drive. The minus sideband components show high sensitivity to the damage condition. 67

88 In order to determine drive amplitudes necessary for accurate localization results, the chosen drive frequencies were varied in amplitude and PSL estimates were made at each drive increment. For the 6 Hz (probing wave), drive levels were varied from -1 db (re 1 N), or.1 N at the low end, to -.25 db, or.9 N at the highest drive level. The low drive (exercising wave) amplitude was kept constant at -8.2 db (.15 N). Figure 3.1 shows the processed angle estimates at each drive condition, for each rosette on the plate. Angle estimates vary in accuracy at low drive levels, becoming more accurate near -3 db of drive amplitude, before deviating again after -2 db. Comparing the strain spectra between the mid-level drive at -3.2 db and the highest drive level at -.25 db (Figure 3.11), the nonlinear components show a clear increase in amplitude as the drive level increases, with the f3 and f2+ showing nearly a 1 db increase at the higher forcing level. The degradation in the localization estimates is likely an effect of a nonlinear damping mechanism, either at the damage location, or at the fixture boundaries. This damping mechanism alters the wave propagation through the rosette location, causing a drop in accuracy at higher drive levels. Reverberation effects could influence the strain measurements, regardless of the drive amplitude. In a steady-state drive condition, the amplitude read by a strain gage will be a superposition of both incoming waves from the source and reflected waves from the boundaries. As damping levels increase, less reflected energy is expected to influence the direct strain measurement, for a given drive amplitude. Nonlinear damping effects, where the damping in the system is drive amplitude dependent, could influence the reverberation characteristics of the plate. In addition, any contact acoustic nonlinearity effect at the plate-fixture interface can contaminate the nonlinear signature from the damage itself, causing the PSL estimates to deviate due to the presence of a second virtual source at the boundary. In an embedded system, a high level of nonlinearity from other regions of the structure may be read by redundant rosettes closer to that area of the airframe. The change in angle estimates, from multiple rosettes over increasing drive levels, may indicate where the effective excitation of one damage condition ends, and the excitation of another damage condition begins. Detection of multiple damage conditions on the same structure was beyond the scope of this study, but remains a consideration for future work. 68

89 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range High Frequency Drive (db re 1 N) Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) High Frequency Drive (db re 1 N) Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) High Frequency Drive (db re 1 N) Figure 3.1: High frequency amplitude sensitivity for the modulated wave angle estimates, in the 3 rows loose, undamped configuration. The most accurate angle result is shown at a high frequency drive amplitude of -3.2 db A similar sensitivity study was conducted to observe the effects of the low frequency exercising wave drive amplitude on the PSL technique. In this case, the high frequency probing wave drive at 6 khz was held constant at -7.2 db, while the low frequency drive was varied from -9.4 db to -1.9 db. PSL angle estimates for each low frequency drive condition are shown in Figure Again, the angle estimates show a clear dependence on the drive level. An inaccurate estimate is shown at -9.4 db, while at -7.3 db, accurate angle estimates are obtained. As the maximum force level is reached, the angle estimates show reduced accuracy, particularly in rosette 2, where the estimate shifts from 28 to -42. Despite the variation in angle estimates over 69

90 Magnitude (db re 1 µ S) Amplitude Spectrum of Strain db Forcing 3.2 db Forcing Frequency (khz) Figure 3.11: Amplitude spectrum of strain rosette 3, gage 1, showing an increase in nonlinear component amplitudes with increasing drive amplitude. A resulting increase in reverberation effects could lead to degradation of the PSL estimate. both the high and low forcing range, overall low force levels appear to be sufficient to drive out the nonlinear response and localize on the induced damage. This is encouraging for embedded airframe applications, where low power requirements are crucial for keeping the aircraft flying within its weight limitations. The low force levels (<1 N in most cases), required for the nonlinear vibration based PSL technique, are easy to achieve with the use of lightweight piezoelectric actuators mounted on the structure. This leads to the use of lightweight amplifier hardware, and therefore less of a burden on the overall operation of the aircraft. The most accurate drive condition, 6 khz at -3.2 db (.48 N) and 75 Hz at -7.3 db (.19 N), was repeated in 1 trials to observe the variation of individual measurements, taken in quick succession. In the damaged condition, the low and high frequency drives were ramped up to the required force amplitudes and a data set was acquired. The drive systems were then ramped down and shut off, before repeating the acquisition process. PSL results from the repeatability study are shown in Figure The result shows a maximum change in angle estimates of approximately 1, with the most variation occurring in rosettes 2 and 3. The overall large size of the 3 rows loose damage increment may contribute to the variation in angle estimates across repeated tests. Because of the large unfastened gap in the plate/stiffener interface ( 16 cm), the nonlinear source may come from various positions along the damaged section of the joint. The strain rosette would then tend to point towards the strongest source 7

91 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range Low Frequency Drive (db re 1 N) Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Low Frequency Drive (db re 1 N) Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Low Frequency Drive (db re 1 N) Figure 3.12: Low frequency amplitude sensitivity for the modulated wave angle estimates, in the 3 rows loose, undamped configuration. The most accurate result is shown at a low frequency drive amplitude of -7.3 db. Past this drive level, nonlinear effects at the boundaries of the structure, as well as nonlinear damping effects, may cause the PSL estimates to degrade. position within the damage footprint. In addition, rosette 3 shows a measurement bias toward the high end of the actual angle range. This indicates that the contact acoustic effect may extend past the range of the unfastened gap, due to the overall decrease in stiffness of the joint. 71

92 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range Trial Number Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Trial Number Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Trial Number Figure 3.13: Repeatability study for the modulated wave angle estimates, in the 3 rows loose, undamped configuration. Steady-state drives consisted of 6 Hz (-3.2 db force amplitude) and 75 Hz (-7.3 db force amplitude). 72

93 With resulting PSL angle estimates for a given damage condition, the SHM system can alert pilots and crews on the ground to both the presence and estimated location of the damage. This allows the aircraft to land before the damage condition worsens. Furthermore, this gives inspectors and maintainers enough information to locate and repair the damage quickly, allowing the aircraft to return to operation without the need for a lengthy visual inspection. The repeatable angle estimate for the 3 rows loose damage increment, in the undamped plate configuration, is illustrated along with the damage footprint in Figure Note that for an embedded system, further statistical processing and automated drive selection (based on the healthy baseline) can lead to more confidence in the estimates of the damage location. Additional rosettes can also help build confidence in the results, particularly in cases where nonlinear effects from the boundaries, multiple damage conditions, or reverberation effects can influence the location estimate. Localization Plot (Total Nonlinear Method) 6 5 Y Position (cm) X Position (cm) Figure 3.14: Repeatable damage localization result for the 3 rows loose, undamped plate configuration. The drive source is shown in green, the vectors from the rosette positions are shown in blue, and the damage location is outlined in red. In an airframe application, this result would allow maintenance crews to easily detect and repair damage without the lengthy downtime associated with visual inspections. 73

94 Row Loose Damage Condition The same frequency selection process was used in evaluating the 1 row loose damage condition, shown in Figure 3.7. The 75 Hz exercising wave frequency was held constant at approximately -6 db, while the probing wave frequency was scanned over the range of 4 khz to 9 khz, at an approximate -3.6 db drive amplitude. Figure 3.15 shows the resulting damaged versus healthy sideband amplitude ratios for the 1 row loose condition. As evidenced by the 14 db and 13 db peak in the f2 responses of gages 1 and 2 respectively, the 5 khz drive condition excites the highest nonlinear response due to the induced damage condition. Increases in amplitudes for the f and f + components are also shown in the damaged condition (Figure 3.16), while other nonlinear components show low signal-to-noise in both healthy and damaged conditions. Note that similar to the 3 rows loose damage increment, low amplitudes are shown for the f 2+ component. This imbalance in corresponding nf ± sideband components could be due to different attenuation effects at the higher frequencies. Recall that to avoid contaminating the PSL estimates with noise in the system, a 1 db threshold was used to filter out the low level nonlinear components from the calculations. Therefore the relatively low signal-to-noise of certain sideband components is not necessarily a concern, provided there is adequate signal at other nonlinear components. Based on the high f2 component increase at 5 khz, this frequency was chosen for amplitude sensitivity studies. For the high frequency drive, forcing amplitude was varied from -9 db to.9 db and PSL estimates were calculated at each force increment. Figure 3.17 shows the resulting angle calculations for each rosette. Note that the actual angle bounds are narrower in this damage condition, compared to the 3 rows loose condition, due to the much smaller damage footprint. Accurate angle estimates are shown at low forcing levels (-9 db to -4.2 db), while at higher drive amplitudes (-3 db to -.6 db) these estimates are degraded. The second rosette in particular shows a large shift in angle estimates, with -2 db drive level resulting in an angle 4 outside the acceptable range. At -1.3 db, all rosette estimates fall out of the accuracy range, while at the highest drive level localization results begin to recover. Inspection of the strain spectra gives insight into another potential mechanism behind the decrease in accuracy at higher drive levels. Figure 3.18 shows the strain spectra for the 45 gage in rosette 2, for both -4.4 db and -1.3 db forcing amplitude. 74

95 A D /A H (db re 1 µ S/µ S) Strain 1 1 Sideband Amplitude Ratio High Frequency A D /A H (db re 1 µ S/µ S) Strain 1 2 Sideband Amplitude Ratio High Frequency f1 f2 f3 f4 f1+ f2+ f3+ f4+ A D /A H (db re 1 µ S/µ S) Strain 1 3 Sideband Amplitude Ratio High Frequency Figure 3.15: Damaged versus healthy sideband amplitude ratios for the 1 row loose damage condition, in the undamped plate configuration. A peak condition is shown at 5 khz, where the f2 sideband component shows >1 db increase in both gages 1 and 2. 75

96 Magnitude (db re 1 µ S) Magnitude (db re 1 µ S) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Amplitude Spectrum of Strain Frequency (khz) db f2 f1 Amplitude Spectrum of Strain 1 3 Damaged Healthy Frequency (khz) Figure 3.16: Damaged versus healthy strain spectra for each gage in rosette 1, using the 5 khz high frequency drive. The f2 sideband components show a >1 db increase in the damaged condition. 76

97 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range High Frequency Drive (db re 1 N) Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) High Frequency Drive (db re 1 N) Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) High Frequency Drive (db re 1 N) Figure 3.17: High frequency amplitude sensitivity for the modulated wave angle estimate, in the 1 row loose, undamped configuration. Accurate angle estimates are shown up to the drive condition where a broadband chaotic response takes place. A broadband chaotic response (similar to that shown in Section 2.6) occurs at the high forcing level, which results in a corresponding drop in accuracy for all angle estimates. The result indicates another benefit in the use of low drive levels for the localization scheme. In the chaotic state, energy from the sidebands leaks into the surrounding broadband response, causing lower sideband amplitudes, and potentially exciting other nonlinear effects, with frequencies in the same band as the sideband components. This can skew the nonlinear amplitudes from the source, read by the strain gages. Driving at lower amplitudes, where the strain spectra exhibit orderly, 77

98 Magnitude (db re 1 µ S) Amplitude Spectrum of Strain db Forcing 4.4 db Forcing Frequency (khz) Figure 3.18: Amplitude spectrum of strain rosette 2, gage 2, showing a transition to a broadband chaotic state at the -4.4 db force level. This has a negative impact on PSL angle estimates when attempting to localize on the damage. discrete sidebands, results in more accurate angle estimates. Once again, this is beneficial for embedded airframe applications, where low profile, lightweight actuators can provide the required force levels for accurate localization. For the low frequency amplitude sensitivity study (Figure 3.19), the 5 khz drive was kept at a constant -6 db, while the 75 Hz drive was varied from -6.4 db to 2.2 db. Angle estimates for this damage condition are accurate starting at -1.5 db and retaining accuracy at the higher drive levels. Contrary to the high frequency amplitude study, the nonlinear response never reaches a broadband chaotic state. Instead, more nonlinear content is steadily driven out at the higher drive levels, resulting in more high signal-to-noise sideband components to use in the PSL estimate. This is also likely to result in more reflected waves influencing the measurement. However, in this case the reverberation seems to have little effect on the estimate at the higher amplitude. This could be due to the use of a near critical drive frequency, and the higher damping associated with the frequency band. Note also that higher drive amplitude is required to achieve accurate localization, compared to the 3 rows loose condition. This is a result of the smaller damage increment, and the higher restoring forces in the joint with 1 loose fastener row. More force is required to drive the contact acoustic effect at the smaller damage footprint. Another implication of the low frequency amplitude study is the idea that a specific selection of both low and high frequency amplitudes may not be necessary 78

99 to yield accurate localization results. In the 1 row loose damage condition, once localization is achieved, increasing the low drive amplitude has little impact on the localization result. Since the nonlinear response is dependent on both the amplitude of the high frequency and low frequency drives, it is possible that the high frequency source can be actively controlled, while the other is provided by natural vibrations present in the system. For instance, in rotorcraft structures the main rotor and tail rotor harmonics could be utilized as a low drive source, while the high frequency is controlled using a compact, low power piezoelectric actuator. This active-passive detection approach would be an effective and lightweight solution for an embedded airframe SHM system. A repeatability study was also conducted on the 1 row loose localization result, as shown in Figure 3.2. Repeating the drive condition of 5 khz (-6 db) and 75 Hz (.5 db), less variation is shown in the angle estimates, compared to the same study conducted on the 3 rows loose damage condition. The smaller damage footprint may contribute to the low scatter (±4 ) of estimates in this configuration. Since nonlinear scattering can occur over less of an area, compared to the larger damage condition, the consistency of the angle result is higher in repeated tests. Figure 3.21 shows the repeatable PSL result for the 1 row loose, undamped plate configuration. The result shows a highly accurate estimate for the relatively small damage size, comparable to a condition on a real airframe where a small region of a joint begins to loosen in the presence of high cyclic loading. 79

100 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range Low Frequency Drive (db re 1 N) Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Low Frequency Drive (db re 1 N) Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Low Frequency Drive (db re 1 N) Figure 3.19: Low frequency amplitude sensitivity in the 1 row loose, undamped plate configuration. The most accurate result is shown at a drive amplitude of.5 db. 8

101 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range Trial Number Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Trial Number Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Trial Number Figure 3.2: Repeatability study for the 1 row loose, undamped plate configuration. Steady-state drives consisted of 5 Hz (-6 db force amplitude) and 75 Hz (.5 db force amplitude). 81

102 Localization Plot (Total Nonlinear Method) 6 5 Y Position (cm) X Position (cm) Figure 3.21: Repeatable damage localization result for the 1 row loose, undamped plate configuration. The PSL estimate accurately detects the small damage size (5 cm x 2.5 cm). 3.3 Summary of Undamped Plate Results Valuable insight was gained on the PSL technique, by experimenting with various excitation methods on the undamped stiffened plate test bed. Single tone steady-state detection techniques were difficult to use, primarily due to the instability of the CAN effect under a steady-state excitation, and reverberation effects in the plate test bed. Because the nonlinear response was highly sensitive to changes in the drive condition, the amplitude and frequency of the excitation could not be easily modified to improve the signal-to-noise of the nonlinear response, and the accuracy of the PSL estimate. The transient method was hampered by low signal-to-noise at the nonlinear components, and overall difficulties in selecting the first group arrival waveform. The modulated wave excitation yielded accurate localization results for both the 3 rows loose and 1 row loose damage conditions, representative of degraded fasteners and loose joints on airframe structures. The technique was influenced by apparent nonlinear damping mechanisms and reverberation effects. The technique also showed degradation due to the observed broadband chaotic response at high drive amplitudes. However, the high and low frequency drive amplitude dependence allowed for the selection of drive conditions with accurate localization results, at low drive levels ( 1 N). An important implication of the drive amplitude studies is the potential use of 82

103 natural vibrations in the airframe as a low frequency source, while a high frequency probing wave is controlled independently to adjust the nonlinear amplitudes. This would be considered an active-passive drive approach as apposed to an active-active approach. The modulated wave method showed particular promise for automation, with interrogation frequencies selected based on direct comparison with a healthy baseline. For these reasons, the modulated wave excitation was the primary focus, as the study moved forward to the damped plate configuration and airframe application. 83

104 Chapter 4 Damped Stiffened Plate Results 4.1 Single Tone Damage Detection Results In order to evaluate the effects of structural damping levels on the localization scheme, single tone damage detection studies were repeated on the damped plate configuration using the 3 rows loose damage increment. It was hypothesized that the added edge damping treatment would absorb energy at the boundaries of the plate, thereby reducing the influence of reflections on the localization method. A range of frequencies was evaluated to again find a drive condition exhibiting a high nonlinear response in the damaged condition. A 22 Hz drive frequency was chosen, similar to the 2227 Hz condition previously used in the undamped configuration (Section 3.1). The steady-state approach was favored over the transient method, due to its higher signal-to-noise at the frequencies with nonlinear response content. Note that the transient localization method was also assessed on the damped plate, but no significant gains were achieved with added damping in the system. This is expected, because the first group arrival was the focus, and therefore reflections from the boundaries would not play an important role. For the same applied force levels, the added edge damping treatment only had the effect of reducing the already low signal amplitudes of the initial waveform. Reflection amplitude levels were also reduced, but localization results remained inaccurate due to overall low signal quality shown by the strain sensors. An example waveform, comparable to the result shown in Figure 3.5, is shown in Appendix A.3. The steady-state single tone technique was further developed on the damped plate configuration by varying force levels with the interrogation frequency of 22 84

105 Hz. This approach was carried out in an effort to observe the effects of amplitude on the single tone CAN response from the damage location. With the added edge damping material, it was assumed there would be minimal effects of nonlinearity from asymmetric stiffness and contact acoustic effects at the boundaries, and that nearly all of the nonlinear response would stem from the damage location itself. Data sets were acquired at 5 force increments, from -1 db to.45 db. Corresponding strain spectra were previously shown in Section 2.6, with chaotic effects dominating the response at the upper force amplitudes. To formally study the effects of the chaotic response on PSL estimates, the f/2, 3f/2, and 5f/2 nonlinear components were tracked as the force amplitude was increased. The resulting nonlinear strain amplitudes from rosette 3 are shown in Figure 4.1. At the lowest force level (-1 db), the f/2 and 3f/2 components show the highest amplitude levels, while the 5f/2 component is buried in the noise. As the drive amplitude increases, each nonlinear component shows a distinct peak at -3.7 db, with a decrease in nonlinear harmonics past this drive level. Figure 4.2 shows the strain spectra at this drive level. Results show the onset of the chaotic response, where energy leaks from the discrete nonlinear components into higher order broadband nonlinearity, and phase relationships become random across the bandwidth. Consequently, the total nonlinear PSL estimates (incorporating strain amplitudes from f/2, 3f/2, and 5f/2), shown in Figure 4.3, show some degradation past this drive level. This reinforces previous observations in the modulated wave approach, where benefits were observed driving with lower force amplitudes. At these lower forcing conditions, the strain response still contains discrete, high signal-tonoise nonlinear components, resulting in higher accuracy angle estimates. Note that there may be potential for more advanced processing schemes to extract localization estimates from the chaotic response. However, the distribution of energy from the nonlinear response over a wide range of frequencies results in more nonlinear signature in regions of the bandwidth where damping is low. Therefore, more energy is likely to be in frequency bands were the level of reverberation in the plate is higher. In these bands PSL estimates are likely to be less accurate as a result. Further processing of the broadband chaotic response for localization was not carried out in the scope of this study. The total nonlinear localization estimate (summing contributions from f/2, 3f/2, and 5f/2) for the -3.7 db drive condition is shown in Figure 4.4. Compared to 85

106 Amplitude (db re 1 µ S) Strain 3 1 Sideband Amplitudes Drive Amplitude (db re 1 N) Amplitude (db re 1 µ S) Strain 3 2 Sideband Amplitudes Drive Amplitude (db re 1 N) f/2 3f/2 5f/2 Noise Amplitude (db re 1 µ S) Strain 3 3 Sideband Amplitudes Drive Amplitude (db re 1 N) Figure 4.1: Subharmonic and ultra-subharmonic amplitudes under increasing force amplitude, with an active drive frequency of 22 Hz in the damped plate configuration. The trend shows a gradual decrease in nonlinear response at the discrete subharmonic and ultra-subharmonic frequencies, once the chaotic response begins at -3.7 db. 86

107 Magnitude (db re 1 µ S) f/2 3f/2 5f/2 Damaged Healthy Frequency (khz) Figure 4.2: Rosette 3, gage 3 strain amplitude spectrum for the 22 Hz single tone excitation, at the -3.7 db drive level. At this point, the nonlinear signatures show the highest signal-to-noise, and therefore damage localization estimates are most accurate. Past this drive level, the broadband chaotic response dominates. the total nonlinear estimate in the undamped configuration (Figure 3.3), an overall more accurate result is shown in the damped configuration. This indicates that the moderate changes in damping over the frequency range of 1 5 khz, due to the added damping treatment, cause more energy absorption at the boundaries of the plate, thereby improving the single tone PSL estimates. While the single tone result is encouraging for built up airframe structure applications (where the damping is typically high), the modulated wave method is still considered the more feasible approach for an embedded SHM system. Regardless of changes in damping, the single tone approach remains highly sensitive to changes in drive frequency and amplitude. As a result, an embedded system would likely have to scan over a wide range of frequencies and amplitudes, with a very fine resolution, to seek out those drive conditions with the highest increase in nonlinear components. A vast database of healthy condition measurements would then be necessary for the comparison with data in the damaged condition. This requires more computing power and storage capacity on the aircraft, or at the ground station, which then in turn requires more data processing capabilities to make the damage assessment in real-time. The modulated wave technique was the primary focus, moving forward on the damped plate configuration, as well as for exploratory studies on the airframe test bed. 87

108 Strain 1 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) 5 5 Angle Estimate Real Angle Range Drive Amplitude (db re 1 N) Strain 2 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Drive Amplitude (db re 1 N) Strain 3 Principal Strain Angle Estimates (Total Nonlinear) Angle (degrees) Drive Amplitude (db re 1 N) Figure 4.3: Drive amplitude sensitivity study for the single tone interrogation at 22 Hz, in the 3 row loose, damped plate configuration. Accurate angle estimates are shown for all rosettes, though slight degradation is observed where the broadband chaotic response takes place, past -3.7 db. This effect is minimal for rosettes 1 and 2, but more prominent for rosette 3. 88

109 Localization Plot (Total Nonlinear Method) 6 5 Y Position (cm) X Position (cm) Figure 4.4: Total nonlinear PSL estimate for the single tone -3.7 db forcing condition, in the damped plate configuration. 4.2 Modulated Wave Damage Detection Results Modulated wave damage detection studies were repeated for the damped plate configuration to study the effects of edge damping treatment on the steady-state PSL technique. As demonstrated in the single tone approach, it was expected the added edge damping treatment would aid in absorbing energy at the boundaries of the plate, resulting in less reverberation influencing localization estimates. Three damage conditions were tested using the modulated wave technique, including the same 3 rows loose condition from previous tests, the same 1 row loose condition near the middle of the joint, and an extra 1 row loose condition closer to the plate boundary. Again, each condition was considered to be a representation of a typical damaged joint condition on an airframe structure. These damage conditions and their corresponding locations are shown in Figure 4.5. The upper plate 1 row loose condition was meant to test a damage position further off the center of the plate, approximately in line with the gage in rosette 1. This would indicate if any error existed in localization results when attempting to detect damage along a or 9 axis of a rosette. The results shown in this section highlight the main distinctions between the PSL localization results in the damped configuration, and those in the undamped configuration. Further results are shown in Appendix A.4. 89

110 Figure 4.5: All tested damage conditions on the damped stiffened plate, using a modulated wave excitation. An extra 1 row loose condition was tested at a position closer to the plate boundaries. Only one damage condition was induced for each tested configuration Rows Loose Damage Condition The process of sweeping through high frequencies in the 3 rows loose damage condition revealed high nonlinear sideband amplitudes at the probing wave frequency of 45 Hz. Once again, higher harmonics of the low frequency were shown to coincide with sidebands around the high frequency drive, potentially enhancing the sensitivity at these nonlinear components. Figure 4.6 shows the damaged versus healthy strain spectra for the selected drive condition. A number of sidebands show 1 db increases between healthy and damaged conditions, notably f 1 and f 1+. Note that compared to the undamped plate condition, where a high drive frequency of 6 Hz was used, very little sideband content is shown in the healthy condition. This indicates a reduction of nonlinearity at the boundaries, due to the added damping treatment. The fact that high amplitude first order sidebands exist only in the damaged condition indicates that these nonlinear effects are purely a result of the induced damage. As a result, varying the drive amplitude of the high frequency was shown to have almost no effect on the PSL angle estimates, and accurate localization results were obtained over the range of forcing levels. The repeatable localization estimate is shown in Figure

111 The level of nonlinearity in the healthy condition can also serve as a quality check for an embedded system, to build further confidence in localization results. The first order sideband terms contain information about the damage extent and position. However, if significant f 1± amplitudes exist in the healthy condition, this signature could contaminate the response from the damage itself, degrading localization estimates. A drive condition showing the purest nonlinear response in the damaged condition is more likely to yield an accurate localization estimate, since all of the nonlinearity can be attributed to the damage. 91

112 Magnitude (db re 1 µ S) Amplitude Spectrum of Strain 2 1 f Frequency (khz) f1+ f2+ Damaged Healthy Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Figure 4.6: Damaged versus healthy strain spectra for each gage in rosette 2, using a 45 Hz high frequency drive. Very little nonlinearity is exhibited in the healthy condition, while the damaged condition shows high sideband content (+1 db for f 1± components). 92

113 Localization Plot (Total Nonlinear Method) 6 5 Y Position (cm) X Position (cm) Figure 4.7: Repeatable damage localization result for the 3 rows loose, damped plate configuration. Accurate estimates are shown over all forcing conditions Row Loose Damage Conditions Evaluating the 1 row loose mid-plate damage condition on the damped configuration, there were initial difficulties exciting a high nonlinear response in the frequency range of 4 9 khz. This was attributed to the added absorption of energy in this frequency range due to the damping treatment. While a 5 khz high frequency drive was previously used to interrogate the 1 row loose condition, it is possible that in the damped structure, not enough energy could be transmitted to the damage location to drive the nonlinear response with this probing wave frequency. To find a new active drive condition, the excitation range was expanded, and the high drive frequency scan was run from 4 khz to 17 khz, in 5 Hz increments. The resulting sideband amplitude ratios are shown in Figure 4.8. A high nonlinear increase of 1 db is shown at the 12 khz drive frequency, while lower frequencies only show amplitude increases on the order of 1 5 db. Negative ratio values down to -5 db are shown at higher frequencies, indicating that some inherent variability must be accounted for in an automated system. Based on the results in this and previous chapters, a minimum of a 1 db increase in nonlinear amplitudes is necessary to indicate a potential drive frequency for effective damage interrogation. Frequencies with amplitude ratios below this threshold were not typically effective in detecting and localizing on the damage. Based on results obtained for the upper-plate 1 row loose damage condition, the 93

114 distance between the drive source and damage appears to have a significant effect on the level of nonlinear response. This is consistent with observations shown in previous modulated wave detection studies [44]. Figure 4.9 shows the sideband amplitude ratios for the upper-plate 1 row loose condition, using the same drive frequency range and amplitudes used on the mid-plate damage. A much higher sideband response is exhibited at the drive frequencies of 12 khz and higher, up to 2 db for each gage. The 12 khz high frequency drive remains the most effective drive condition for exciting the high nonlinear response at the damage, based on its significant increase in sideband content. The corresponding strain spectra for the upper-plate damage, in the 12 khz drive condition, are shown in Figure 4.1. The strain response exhibits high sideband responses in the damaged condition ( 2 db), and minimal sidebands in the healthy condition, apart from the first order components. It is possible that at this high drive frequency, the f 1± components are influenced by nonlinearity of the active drive system. In addition, the gaps between fastener rows on the stiffened joint could contribute to the nonlinearity using this high drive condition. At 12 khz, the induced bending wavelength of the plate is approximately 4.5 cm, closely matching the 5 cm gap between fastener locations on the plate. As a result this drive condition is likely to exercise some nonlinear response at the gaps, which could manifest itself in the first order sideband response. As in previous tests, force amplitude sensitivity studies were carried out on both 1 row loose damage conditions, in order to determine effective force levels for localization. These final angle estimates are illustrated in Figure Compared to the undamped configuration, higher force amplitudes were necessary for the probing wave frequencies, while lower forcing was required for the exercising wave. In the undamped plate configuration, 5 khz and 75 Hz were driven at amplitudes of -6 db and.5 db, respectively. In the damped configuration, for the same damage increment, 12 khz and 75 Hz were driven at amplitudes of 8.8 db and -4.4 db, respectively. Meanwhile, the upper-plate 1 row loose damage condition required drive amplitudes of 6.5 db and -3.7 db for the 12 khz and 75 Hz excitations, respectively. The changes in drive frequencies and amplitudes required to obtain an accurate localization estimate are expected, when interrogating similar damage sizes in different positions on the plate, and in different damping conditions. The added damping appears to absorb enough energy at 5 khz, that this frequency is no longer effective, over the investigated force range, to produce the nonlinear response in the 1 row loose damage condition. 94

115 A D /A H (db re 1 µ S/µ S) Strain 3 1 Sideband Amplitude Ratio High Frequency (khz) A D /A H (db re 1 µ S/µ S) Strain 3 2 Sideband Amplitude Ratio High Frequency (khz) f1 f2 f3 f4 f1+ f2+ f3+ f4+ A D /A H (db re 1 µ S/µ S) Strain 3 3 Sideband Amplitude Ratio High Frequency (khz) Figure 4.8: Damaged versus healthy sideband amplitude ratios for the 1 row loose midplate damage condition, in the damped plate configuration. A peak nonlinear response is shown at 12 khz, where the f3 sideband shows an 8 db increase in all gages. Other frequencies show high increases in response, but not over all gages in the rosette. This led to selection of the 12 khz drive condition for further study. 95

116 A D /A H (db re 1 µ S/µ S) Strain 2 1 Sideband Amplitude Ratio High Frequency (khz) A D /A H (db re 1 µ S/µ S) Strain 2 2 Sideband Amplitude Ratio High Frequency (khz) f1 f2 f3 f4 f1+ f2+ f3+ f4+ A D /A H (db re 1 µ S/µ S) Strain 2 3 Sideband Amplitude Ratio High Frequency (khz) Figure 4.9: Damaged versus healthy sideband amplitude ratios for the 1 row loose upperplate damage condition, in the damped plate configuration. A peak nonlinear response begins near 12 khz, with the f2 component showing a 2 db increase in the damaged condition. This is the highest increase shown over all drive conditions at this damage configuration. 96

117 Magnitude (db re 1 µ S) Amplitude Spectrum of Strain 2 1 f2 f4 f1 f1+ f2+ f3+ Damaged Healthy Frequency (khz) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Figure 4.1: Damaged versus healthy strain spectra for each gage in rosette 2, using a 12 khz high frequency drive for the upper-plate 1 row damage condition. Sideband amplitude increases are shown for all ± sidebands in the response. 97

118 Localization Plot (Total Nonlinear Method) Localization Plot (Total Nonlinear Method) Y Position (cm) Y Position (cm) X Position (cm) X Position (cm) (a) Mid-plate, 1 row loose. (b) Upper-plate, 1 row loose. Figure 4.11: Repeatable damage localization results for the (a) mid-plate and (b) upper plate 1 row loose damage conditions, in the damped plate configuration. Compared to the undamped plate, higher frequencies and adjustments in forcing are required to excite the high nonlinear response, and to localize on the damage. However, increasing the drive frequency and tuning the force levels helps regain the 1 row loose localization capability in the damped configuration. Changes in force levels are necessary, possibly to regain some of the displacement levels at the damage location, since less deflection is expected at higher frequencies. Increasing the force amplitude levels of the probing wave may help to penetrate the damage location, resulting in more nonlinear response. Despite the increase in required forcing, these amplitude levels, less than 1 N in magnitude, are still attainable using lightweight actuators in an embedded application. The chosen actuators must have the capability to interrogate a wide range of frequencies, at varying force levels, in order to exercise the most effective drive conditions for detection and localization. Higher frequencies and forcing may be necessary to interrogate the damage, depending on the damping levels present in the system. 98

119 4.3 Summary of Damped Plate Results In the damped plate configuration, successful detection and localization results were obtained for both the single tone and modulated wave excitation methods. In the single tone approach, damping treatment appeared to cause more absorption of energy at the plate boundaries, leading to less reverberation effects, and enhanced localization capability in the steady-state condition. Varying force levels on the 22 Hz drive condition, the resulting chaotic response at higher drive amplitudes created difficulties for the automation algorithm. The high energy from discrete nonlinear frequencies leaked into the broadband nonlinear response, and a decrease in localization accuracy was seen as a result. In an automated system, this chaotic response could be monitored and mitigated by limiting the active drive amplitudes in both single tone and modulated wave approaches. The modulated wave PSL algorithm was shown to be effective in the damped configuration, though adjustments in drive frequency and forcing were necessary to induce the most effective nonlinear drive condition (the condition showing the highest nonlinear response in the presence of damage). Further insight may be gained by studying the bending wave dispersion curve for the plate structure. Wavelengths were plotted, corresponding to a wide range of bending wave frequencies, alongside the acoustic wavelength. Damage sizes and drive conditions were shown on the same curve in order to observe the overall relation between localization drive conditions, damage sizing, and the acoustic properties of the plate structure. This relationship is shown in Figure The critical frequency of the plate is shown where the grazing acoustic wavelength and plate bending wavelength curves intersect, near 48 Hz. Nearly all of the drive conditions used to obtain accurate PSL results lie at or near the critical frequency, the point of highest acoustic radiation damping on the plate structure. Given that this is the point of the largest direct field radius in the plate, it is logical that the most accurate localization results occur when driving the system near this frequency. This, combined with the added damping treatment, can lead to lower reverberation effects, lower nonlinearity from the boundary conditions, and a sideband response that is indicative of only the level of damage present in the system. 99

120 1 4 Aluminum Plate Wavelengths Wavelengths (cm) Rows Loose Damage Size Damped PSL Drive Conditions 1 Row Loose Damage Size Frequency (Hz) c Beff c L c S Undamped PSL Drive Conditions c air Stiffener Width Damage Size Figure 4.12: Wavelength dispersion curves for the aluminum plate test bed. All damage sizes assessed in the damped and undamped configurations are marked according to their relative size and matching wavelength on the curve. The best PSL drive conditions are shown at 6 khz (undamped, 3 rows loose), 5 khz (undamped, 1 row loose), 4.5 khz (damped, 3 rows loose), and 12 khz (damped, 1 row loose). The majority of localization estimates were made using excitation frequencies near the critical frequency of the plate, at 4.8 khz, where radiation losses are the highest. In an airframe application, the high damping of the built-up structure could be a benefit to the PSL technique. The isolated plate structure naturally exhibits high reverberation due to its limited size and fixed boundary conditions. However, the inherent size and complexity of a real airframe structure gives the vibration energy more paths to follow, and more energy is likely to flow towards natural sinks in the system. Nonlinear signatures from the damage are less likely to reflect from the boundaries and influence the localization estimate. The application of the PSL technique to a real airframe structure is explored in Chapter 5. 1

121 Chapter 5 Airframe Applications 5.1 Rotor Blade Passage as a Low Frequency Source Since the wave modulation technique requires the use of two drive frequencies, an embedded active-active drive system would require separate low and high frequency actuators. This can lead to higher weight impacts on the structure, since low frequencies are often difficult to drive without a heavy shaker apparatus. While previous tests used a constant 75 Hz low drive frequency, it was hypothesized that the modulated wave approach could use nearly any low frequency to exercise the damage location, provided enough force could be applied at that forcing frequency. On an operational aircraft, low frequency energy is present due to a number of natural sources in the system. For instance, the main rotor and tail rotor systems provide very high amplitude vibrations at their associated blade passage frequencies and higher harmonics. For an embedded SHM system, these systems could be used as the low frequency input (exercising wave) in a nonlinear modulated wave approach, while a lightweight piezoelectric actuator provides the high frequency probing wave excitation for the structure. This active-passive modulated wave approach was explored using the collocated shaker system on the damped stiffened plate structure. As in previous studies on the plate test bed, the 3 rows loose condition was evaluated first. A high frequency of 25 Hz was identified for its high nonlinear response in the damaged condition, based again on increases in sideband amplitudes from healthy to damaged conditions. The corresponding damaged versus healthy strain spectrum for rosette 1, gage 1, is shown in Figure 5.1. Various higher order sideband components (up to f1±) show high amplitude gains in the damaged 11

122 condition. Focusing only up to the f 4± components resulted in a poor localization estimate, likely due to the exclusion of information from the higher order components. Varying high frequency and low frequency amplitudes, a repeatable localization result was obtained by taking into account contributions up to f 8±. Magnitude (db re 1 µ S) Amplitude Spectrum of Strain Frequency (khz) Figure 5.1: Example damaged versus healthy strain spectra for gage 1 in rosette 1, using Amplitude Spectrum of Strain 1 2 a 25 Hz 1 high drive frequency, with a UH-6 rotor blade passage frequency of 17 Hz. Components up to f8± were used for the total nonlinear estimate. 2 Magnitude (db re 1 µ S) Frequency (khz) Amplitude Spectrum of Strain 1 3 enough energy 1 at the low frequency to exercise the damage condition, due to the high Magnitude (db re 1 µ S) f8 f1 f1+ f8+ Damaged Healthy The repeatable angle estimates for both 3 rows loose and 1 row loose damage conditions are shown in Figure 5.2. For the large damage increment, 25 Hz was driven at -7.2 db, while 17 Hz was driven at 4 db. In the 1 row loose condition, a 3 Hz excitation was driven at -8.8 db, while 17 Hz was driven at 5.6 db. The higher forcing required for the low drive frequency indicates that further exercising of the damage location is required to excite the nonlinear response in the 1 row loose condition. Note that in a real airframe structure, there would be more than amplitude vibrations from the rotor system. If active vibration controllers are installed, these could also be utilized to provide a low frequency source for the system. The high frequency probing wave could be controlled independently to achieve the desired nonlinear response for the PSL method. The system could also evaluate the number of sideband components 5 present in the damaged condition, so that valuable information about the damage is not overlooked in the processing scheme, due to exclusion of Frequency (khz) higher order nonlinear components. The accurate localization results obtained in both damage conditions show the feasibility of utilizing this active-passive modulated wave technique in an embedded SHM application. 12

123 Localization Plot (Total Nonlinear Method) Localization Plot (Total Nonlinear Method) Y Position (cm) Y Position (cm) X Position (cm) X Position (cm) (a) 3 rows loose. (b) 1 row loose. Figure 5.2: Repeatable damage localization results for the (a) 3 rows loose and (b) 1 row loose damage conditions. Each condition was assessed using the UH-6 blade passage frequency as a low drive source. A high frequency of 25 Hz was used in the 3 rows loose condition, while 3 Hz was used in the 1 row loose condition. These are comparable to previous 3 rows loose (Figure 4.7) and 1 row loose (Figure 4.11) results on the damped plate configuration. 5.2 UH-6 Upper Cabin Testing Experimental Setup and Procedure Having tested the modulated wave PSL damage detection and localization method on the stiffened aluminum plate, a more representative set of tests was designed and carried out on the UH-6 upper roof cabin test bed (Figure 5.3). The primary objective was to explore the use of the developed technique on a realistic airframe structure, featuring complex geometry and high structural damping. A region of the airframe was chosen for testing, based on the fact that the original I-beam frame structure had been removed. This allowed for the fabrication of a simple stiffener, which was added to the skin structure using existing bolt holes at the original skinstiffener joint location. A detailed view of the tested region is shown in Figure 5.4. The fabricated C-channel stiffener was 3 cm wide, and 3.5 cm in length. Fasteners were positioned approximately at 2 cm increments along the joint, and damage was induced by fully loosening various fasteners. As in the plate test bed, the loose fasteners were representative of working rivet conditions in the airframe, but were highly repeatable by tightening to the same torque conditions for subsequent healthy 13

124 Figure 5.3: UH-6 transmission frame test bed. The tested region of the airframe, a simulated skin-stiffener joint, is outlined in red. evaluations. Loose fastener damage conditions, featuring both 6 and 4 loose fasteners, were tested. The 4 loose condition was assessed in two positions along the joint. The 6 loose condition resulted in a 12 cm gap in the skin-stiffener joint, while the 4 loose condition was 7.5 cm in length. The aluminum skin was instrumented with 2 strain sensor rosettes, on opposite sides of the stiffener damage feature. As in the previous plate testing, a collocated Wilcoxon F4/F7 shaker assembly was used to provide the low frequency exercising wave and high frequency probing wave excitations. The shaker was mounted in a free standing upright configuration on the nearby beam structure, using a heavy fastener, a bolt hole from a previous structural joint, and the threaded mounting hole on the shaker itself. Due to the upright orientation, an impedance head was not used to monitor force levels. However, drive parameters were monitored by recording amperage to the electromagnetic F4 shaker, and voltage supplied to the piezoelectric 14

125 Figure 5.4: Experimental setup for PSL testing on the airframe skin structure. A c-channel stiffener was added to the skin using existing bolt holes. The shaker was mounted to the nearest I-beam feature in a free-standing configuration. 2 strain rosettes were mounted on the.75 in thick skin to detect induced damage conditions. Both 6 loose (outlined in red) and 4 loose conditions (outlined in yellow) were tested. F7 shaker, since forces output from these shakers were directly proportional to these quantities. Based on previous testing, and blocked force output shaker specifications provided by the manufacturer, the maximum current of 1.4 A supplied to the F4 shaker was expected to yield less than 1 N of force. The maximum voltage supplied to the F7 shaker throughout the upper cabin testing was limited to 2 V, or a maximum force output of approximately 5 N. These force levels are attainable using various commercially available piezoelectric elements, more lightweight and practical for embedded applications than the collocated shaker apparatus. For an initial selection of frequencies, the bending wavelength dispersion relations were referenced for the.75 in aluminum skin (Figure 5.5). The 75 Hz bending wavelength was observed to be on the order of the largest damage size, and based on the previous use of this drive frequency on the plate test bed, it was again chosen for initial testing on the airframe. High frequencies were scanned from 4 khz to 12 khz, in 5 Hz increments. In establishing the initial healthy baseline data, and performing the subsequent scan in the damaged condition, higher initial drive levels were used, compared to those used in the stiffened plate test bed. The 75 Hz low frequency 15