Proceedings of the ME Conference on mart Materials, daptive tructures and Intelligent ystems MI eptember 8-,, cottsdale, rizona, U MI- PREDICTIVE MODELING OF PCE TRUCTURE FOR HM WITH PW TRNDUCER Matthieu Gresil Bin Lin Yanfeng hen Victor Giurgiutiu LM, Department of Mechanical Engineering, University of outh Carolina, Columbia, C, U I. BTRCT This paper presents an investigation of predictive modeling of space structures for structural health monitoring (HM) with piezoelectric wafer active sensors (PW) transducers. The development of a suitable HM system for complex space structure is not trivial; creating a robust HM capability requires at least: flexible accommodation of numerous configurations; detection of damage in complex multifunctional structures; (c) identification if mechanical interfaces are properly connected. To realize this, we propose a predictive modeling approach using both analytical tools and finite element method (FEM) to study the health status of the structure, the power and energy transduction between the structure and the PW. fter a review of PW principles, the paper discusses the modeling and the power and energy transduction between structurally guided waves and PW. The use of guided wave (GW) and the capability of embedded PW to perform in situ nondestructive evaluation (NDE) are explored. FEM codes are used to simulate GW of D and 3D space structure using the commercials software BQU. PW transducers placement at different location on a flat plate and on an isogrid panel was simulated. The signal scattered by a crac emerging from the hole is simulated. Predictive modeling of power and energy transduction is discussed using an analytical approach. This model of -D power and energy transduction of PW attached to structure allows examination of power and energy flow for a circular crested wave pattern. Wave propagation method for an infinite boundary plate, electromechanical energy transformation of PW and structure, and wave propagation energy spread out in -D plate are considered. The parametric study of PW size, impedance match gives the PW design guideline for PW sensing and power harvesting applications. II. INTRODUCTION tructural health monitoring is an emerging technology with multiple applications in the evaluation of critical structures. The goal of HM research is to develop a monitoring methodology that is capable of detecting and identifying, with minimal human intervention, various damage types during the service life of the structure. typical monitoring system would be one which enables non-invasive, continuous monitoring of the structure. Numerous approaches have been utilized in recent years to perform structural health monitoring; they can be broadly classified into two categories: passive and active methods. ctive HM systems using interrogative Lamb waves are able to cover large areas from a single location maing such systems cost effective and efficient. nother advantage is that Lamb waves provide through-the-thicness interrogation which allows detection of internal defects in materials. Piezoelectric wafer active sensors (PW) are used for active HM technique. However, Lamb waves present some difficulties: they are dispersed, at a given frequency, and thus several modes can propagate at different speeds. Wor has be done to establish analytically the dispersion curves [-6], to validate experimentally [7] and to study the effect of dispersion over long distances [8]. The phenomena of interaction between the ultrasonic wave and the defect and/or the structure, leading to a complex signature (reflection, diffraction, mode conversion, etc.) must be simulated to achieve a specific response signal actually received by sensor. Many authors have already investigated the interaction of Lamb modes with a single defect lie crac, notch or circular cavity. ome of them used analytical [9] or semi-analytical [] resolutions. Whereas many authors [-7] chose the most popular computational tool used in engineering research and industrial design, the finite element method (FEM). Finite element method (FEM) modeling has a role to play in simulating elastic wave propagation associated with acoustic phenomena and ultrasounds problems. This paper presents the use of guided wave (GW) and the capabilities of embedded PW to perform in situ nondestructive evaluation (NDE) are explored. FEM codes are used to simulate GW of D and 3D space structure. PW Copyright by ME
transducers placement at different location on a flat plate and on an isogrid panel was simulated. The signal scattered by a crac emerging or not from the hole is simulated. Predictive modeling of power and energy transduction is discussed using an analytical approach. This model of -D power and energy transduction of PW attached to structure allows examination of power and energy flow for a circular crested wave pattern. III. NLYTICL MODEL Piezoelectric wafer active sensors (PW) are the enabling technology for active and passive HM systems. PW couples the electrical and mechanical effects through the tensorial piezoelectric constitutive equations s T d E () E ij ijl l ij D d T E () T j jl l j where, ij is the mechanical strain; T l is the mechanical stress; E is the electrical field; D j is the electrical displacement; E s ijl is the mechanical compliance of the material measured at T zero electric field ( E ), j is the dielectric permittivity measures at zero mechanical stress ( T ), and d ij represents the piezoelectric coupling effect. PW utilize the d 3 coupling between in-plane strain and transverse electric field. 7-mm diameter PW,.mm thin, weights around 78 mg and costs around $ each. PW are lightweight and inexpensive and hence can be deployed in large numbers on the monitored structure. PW transducers can be serve several purposes [8]: high-bandwidth strain sensors; high-bandwidth wave exciters and receivers; (c) resonators; (d) embedded modal sensors with the electromechanical impedance spectroscopy method. By applications types, PW transducers can be used for (i) active sensing of far field damage using pulse-echo, pitch-catch, and phased-array methods, (ii) active sensing of near field damage using high frequency EMI and thicness gage mode, and (iii) passive sensing of damage-generating events through detection of low-velocity impacts and acoustic emission at the tip of advancing cracs. The analytical modeling of the pitch-catch process between two PW transducers separated by a distance x was carried out in frequency domain in four steps: (i) Fourier transform the time-domain excitation signal Ve () t taen into the frequency domain spectrum, Ve ( ); (ii) calculate the frequency-domain structural transfer function at the receiver location, Gx (, ) ; (iii) multiply the structural transfer function by frequencydomain excitation signal to obtain the frequency domain signal V x, G x, V ; (iv) perform at the receiver, i.e., r inverse Fourier transform to obtain the time-domain receiver signal, V ( x, t) IFFT{ V ( x, )} IFFT{ G( x, ) V ( )}. r r e e In this paper, the main interest is in symmetric fundamental mode ( ) and anti-symmetric fundamental mode ( ). For Lamb waves with only two modes ( and ) excited, the G is given by Eq. (99) of ref. structure transfer function [8], page 37, which gives the in-plane strain at the plate surface as a x, yd (sin ) ' D N x t i a e o, can be written as N a i xt i (sin a) e ' D i x i x i xt (3) G e e (4) N () a i (sin a) D ' N (6) a i (sin a) D ' D d d d d d (7) (, ) cos sin 4 sin cos D d d d d d (8) (, ) sin cos 4 cos sin N cos( d)sin( d) (9) N sin( d)cos( d) () cp () cs where a is the half length of the PW, d is the half thicness of the plate, is the shear stress between PW and the plate, is Lame s constant, and are the wavenumbers for and respectively, x denotes the distance between the two PW transducers, represents the wavenumber for or accordingly, c p and c s are the wave speed for pressure wave and shear wave respectively. In the transfer function, it could be observed that and will determine the amplitude of and mode. In both and sin sin a, in which terms, there is a and represent the tuning effect. The wave speed dispersion curve is obtained by solving Rayleigh-Lamb equations, which are transcendental equations that require numerical solution. The usual form of Rayleigh Lamb equations is as D, d and D d, () Copyright by ME
fter getting the wave speed dispersion curve, the wavenumber for each frequency component i.e. c is nown. Thus, all the terms involved in the plate transfer function could be solved, and the plate transfer function G( ) is obtained. fter the plate transfer function G( ) is obtained, the excitation signal is Fourier transformed. IV. FEM MODELING In non-destructive evaluation (NDE), a common understanding is that the ultrasonic scanning technique can usually detect damage. Furthermore the fundamental anti-symmetrical mode ( ) is preferable and more sensitive to damage because its wavelength is shorter than that of the mode at the same frequency. However, the mode exhibits more dispersion at low frequencies. The FEM simulation of the mode requires fine spatial discretization with substantial computational cost for the sae of the short wavelength. In contrast, the mode shapes of the mode are simpler and the stresses are almost uniform throughout the thicness of the plate at low values to the frequency and plate thicness product. For these reason, the two modes and were selected in this study to evaluate the interaction of Lamb waves with different defect. The analytical modeling, the finite element modeling and the experimental results for a -mm thic aluminum plate with -mm PW distance for a frequency of Hz are shown in Figure. and mode wave pacages could be observed. The wave speed of mode is higher than the mode, so the wave pacet is piced up earlier than the wave pacet. Furthermore, the different results show a near-perfect match.. D modeling of realistic rib-stiffened structure The geometry of the model was chosen based on the approximate rib spacing, sin thicness, and rib dimensions found in the isogrid structures described in various publications [9, ]. pplication of the HM method on a complex structure was investigated utilizing a simulated satellite panel from two aluminum (66-T6) plates with a dimension of 44 x mm. In order to realistically represent a complex satellite structure, an isogrid frame composed of sixty-four x 9 mm cutouts with a mm wall thicness was modeled. For the purpose of this study, Lamb wave are considered, which travel in wave guides and activate the entire thicness of the structure. In plates, symmetric and anti-symmetric wave modes are possible and travel at velocities dependent on frequency, and the thicness of the plate. The dispersion characteristics of a 3-mm thic plate are shown in Figure. s shown in this figure, for a frequency below Hz, only two modes are presents: the fundamental symmetric mode and the anti-symmetric mode. Moreover for a frequency below 6 Hz, the mode travels faster than the mode. The commercial finite element analysis software BQU was used to investigate the same geometry as described before for a D model (Figure 3). Because of the dynamic wave propagation events, BQU explicit was used for its time calculation efficiency. For model simplification and because the piezoelectric elements are not available in BQU/Explicit, the actuation was applied as a pair of self-equilibrating forces. The geometry was meshed with C3D4R (plane strain element, 4-node bilinear, reduced integration). Preliminary D and D wor on a simple plate indicated that the best match between experiments and FEM was obtained using the default viscous damping parameters of the BQU software. The time modulation applied to the self-equilibrating excitation forces was a 3 count 3-Hz smoothed tone burst; preliminary tests indicated that this excitation frequency generates well separated and wave pacets. Figure 4a presents a comparison between the finite element analysis results for a plate (without rib) and with one rib. The receiver PW (R-PW) is at -mm of the transmitter PW (T-PW), and the rib (mm x 9 mm) is on the middle of the path. On this figure, the mode does not change, whereas of the mode does change. Moreover, some mode conversion and some reflections can be observed when the rib is present. Figure 4b presents a comparison between the finite element analysis results for a plate (without rib) and with two ribs. The R-PW is at -mm of the T-PW, and the first rib is at mm and the second rib is at 7 mm of the T-PW. On this figure, the mode does not change, whereas the mode does change. Moreover, some mode conversion and some reflections can be seen in the signal when two ribs are present in the path between the T-PW and the R-PW. In order to detect damage in the structure, a crac was modeled at the corner on the rib and the plate (Figure ). The size of the crac is.-mm length and.-mm thic. mall changes in the signal received at R and R-PW are observed. Figure 6a presents a comparison of R-PW signal in the pristine plate and in the plate with corner crac at rib. The mode does not change. The mode does change slightly with its magnitude decreasing a little in the case of the crac. Figure 6b presents the results for R-PW: again, the mode does not change; the mode changes slightly: its magnitude decreases, but less than for the R-PW. This predictive D FEM analysis shows the importance of sensors positioning to achieve good crac detection in a complex structure. B. 3D modeling of realistic rib-stiffened structure for space application To test the application of the HM method on a realistic 3D complex structure we considered a simulated rapid satellite panel consisting of two isogrid structures. Each isogrid was 3 obtained by maing 64 cutouts ( xx9mm with mm 3 wall thicness) in a 44x 44xmm aluminum 66-T6 plate. bolt hole was drilled in the center of each grid (Figure 7). PW transducers were applied to the isogrid (Figure 7b). The R-PW is at -mm from the T-PW, whereas the R- PW is at ~77-mm from the T-PW. small crac was simulated in one of the bolt holes (Figure 7c). 3 Copyright by ME
The excitation signal was again a 3-count 3-Hz smoothed tone burst. Figure 8 present a comparison of the signals predicted for the pristine structure and for the structure with a craced hole. Figure 8a, shows the signal captured by R-PW very clear signal change is observed due to the crac in the hole (time shift, and magnitude decrease). Moreover, many modes conversion and many reflections are present in the 3D model which greatly complicates the analysis of these data. Figure 8b presents the predicted signals captured by the R-PW: the signal change due to the crac is much less than R-PW. This 3D predictive FEM analysis shows the critical importance of sensors positioning for the detection of crac in a complex structure. The predictive modeling results presented here should be compared with actual an experimental data taen an actual isogrid panel. V. PREDICTIVE MODELING OF POWER ND ENERGY TRNDUCTION FOR HM PPLICTION preliminary analysis of the -D and -D power and energy transduction process for HM applications was performed [, ] by considering PW transmitter; PW receiver; and (c) PW transmitter-receiver pair. Both -D linear PW and -D circular PW analytical models of wave propagation and power and energy transduction were based on the following assumptions: ideal bonding connection between PW and structure; ideal excitation source at the transmitter PW and fully-resistive external load at the receiver PW; and (c) axial and flexural wave propagation. The electrical active power, reactive power, and power rating for harmonic voltage excitation were examined. The parametric study of transmitter size and impedance, receiver size and impedance, and external electrical load gives the PW design guideline for PW sensing and power harvesting applications. The analysis was performed in the simplifying case of axial and flexural waves, which are easier to handle than the full guided-wave model. However, the principles of this exploratory study can be extended without much difficulty to the full multi-mode guided-waves. brief summary of -D model is given next.. Circular PW Transmitter Power and Energy The electrical energy of the input voltage applied at the PW terminals is converted through piezoelectric transduction into mechanical energy that activates the expansion-contraction motion of the PW transducer. This motion is transmitted to the underlying structure through the shear stress in the adhesive layer at the PW-structure interface. s a result, ultrasonic guided waves are excited into the underlying structure. The mechanical power at the interface becomes the acoustic wave power and the generated axial and flexural waves propagate in the structure. It was found that the reactive electrical power required for 7-mm diameter circular PW excitation is orders of magnitude larger than the active electrical power. Hence, the power rating of the PW transmitter is dominated by the reactive power, i.e., by the capacitive behavior of the PW. We note that the transmitter reactive power is directly proportional to the transmitter admittance ( Y ic ), whereas the transmitter active power is the power converted into the ultrasonic acoustic waves generated into the structure from the transmitter under perfect bonding assumption. The power analysis indicated that the active power applied by the transmitter PW converts to circular crested wave power. Perfect electrical source and loss-less adhesive layer was assumed in this model and there is no loss during the electricalmechanical-wave power transduction. The power analysis also indicated that optimal axial and flexural wave excitation by PW can be obtained when the PW radius is an odd multiple of the half wavelength of particle wave modes. The geometric tuning can be obtained through matching between their characteristic direction and the half wavelength of the excited axial or flexural wave mode. Due to the tuning effects, a remarable variation of active power with frequency is shown in analysis. We notice that the active power (i.e., the power converted into the ultrasonic waves) is not monotonic with frequency, but manifests peas and valleys. s a result, that ratio between the reactive and active powers is not constant, but presents the peas and valleys pattern. The increase and decrease of active power with frequency corresponds to the PW tuning in and out of various ultrasonic waves traveling into the structure. Figure 9presents the results of a parameter study for various radius circular PW sizes and frequencies. The resulting parameter plots are presented as 3D mesh plots. Figure 9a presents a 3D mesh plot of the power rating vs. frequency and transmitter radius: for a certain transmitter radius, the power rating increases when the frequency increases. For a given frequency, the power rating increases when the transmitter radius increases. These results are clarifying: to drive a -mm length PW at Hz with a V constant voltage input, one needs a power source providing W of power. Figure 9b shows the wave power that PW generates into the structure; tuning effect of transmitter size and excitation frequency are apparent; a larger PW does not necessarily produce more wave power at a given frequency! The maximum wave power output in this simulation is ~ mw. The powers contained in the axial waves and flexural waves are given separately in Figure 9c and Figure 9d. In some PW HM applications, a single mode is often desired to reduce signal complexity and simplify signal interpretation and damage detection. Figure 9c shows the frequency-size combinations at which the axial waves are maximized, whereas Figure 9d indicates the combinations that would maximize the flexural waves. These figures give useful guidelines for the choosing PW size and frequency values that are optimum for selecting a certain excitation wave mode. This study gives guidelines for the design of transmitter size and excitation frequency in order to obtain maximum wave power into the HM structure. 4 Copyright by ME
B. Wave power and energy transfer from transmitter in structure The power and energy of forward and bacward axial and flexural waves remain constant in -D situation. However, the axial and flexural wave excited by circular PW transmitter spreads out. Kinematic analysis gives the displacement generated by a circular PW in terms of the axial and flexural displacement as with Bessel function. Bessel function can be approximated using the fact that it exhibits an asymptotic behavior after four or five cycles of the wavelength of the mode considered. The total axial and flexural wave is independent with the wave propagation distance r. The displacement amplitude exhibits an asymptotic behavior with r. C. Circular PW receiver Receiver PW has a similar size tuning effect as transmitter PW. When propagating waves reach the receiver PW, receiver PW converts the wave energy to electrical energy and outputs a voltage signal. For sensing application, a high value of the output voltage is desired. The external electrical load such as oscilloscope resistance is set to high impedance. In this case, only a small amount of power and energy is piced up by PW. In power harvesting application, receiver PW with a matching external electrical load impedance can output the maximum power. D. Circular PW Pitch-catch Power nalysis The power and energy transduction flow chart for a complete pitch-catch setup is shown in Figure. There are three parts in the power flow: transmitter PW power and energy, wave propagation power and energy in structure, and receiver PW power and energy. In pitch-catch mode, the power flow converts from electrical source into piezoelectric power at the transmitter, the piezoelectric transduction converts the electrical power into the mechanical interface power at the transmitter PW and then into acoustic wave power travelling in the structure. The wave power arrives at the receiver PW and is captured at the mechanical interface between the receiver PW at the structure. The mechanical power captured is converted bac into electrical power in the receiver PW and captured at the receivers electric instrument. The time-averaged electrical power, mechanical power at the transmitter and wave power can be calculated from the frequency response function. In a -D pitch-catch sensing simulation, we used an luminum alloy 4 infinite plate with mm thicness. PW transmitter and receiver were 7-mm diameter and.-mm thicness. -Vpp -Hz central frequency 3-count Hanning window tone-burst signal was applied to the transmitter. The receiver instantaneous voltage response was shown in Figure a. The fast axial wave was separated from the low speed flexural wave. The axial wave was nondispersive and ept the shape of excitation signal. The flexural wave spreaded out due to the dispersive nature. The receiver V dt RM power, defined as RM, was calculated (Figure b). It is clear that the receiver RM power is proportional with r. VI. CONCLUION This paper presented an investigation of predictive modeling of space structures for structural health monitoring (HM) with piezoelectric wafer active sensors (PW). The development of a suitable HM system for complex space structure is not trivial; creating a robust HM capability requires at least: flexible accommodation of numerous configurations; detection of damage in complex multi-functional structures; (c) identification if mechanical interfaces are properly connected. To realize this, we propose a multi-physics predictive modeling approach using both analytical tools and finite element method (FEM) to study the health status of the structure and the power and energy transduction between the structure and the PW. fter a review of PW principles, the paper was discussed the modeling and the power and energy transduction between structurally guided waves and PW. The use of guided wave and the capability of embedded PW to perform in situ nondestructive evaluation were explored. FEM codes were used to simulate GW of a D and a 3D space structure using the commercial software BQU. PW transducers placement at different location on a flat plate and on an isogrid panel was simulated. The signal scattered by a crac emerging from the hole was simulated. Predictive modeling of power and energy transduction is discussed using an analytical approach. This model of -D power and energy transduction of PW attached to structure allows examination of power and energy flow for a circular crested wave pattern. Wave propagation method for an infinite boundary plate, electromechanical energy transformation of PW and structure, and wave propagation energy spread out in -D plate are considered. The parametric study of PW size, impedance match gives the PW design guideline for PW sensing and power harvesting applications. The analytical model is expected to be extended to 3D circular PW analysis, and Bessel function will studied and included in future wor to realize guided wave propagation between two circular PW transducers. For further study, the analytical modeling is expected to include damage in the plate structure using a non-linearity aspect. Moreover the non-linear element will be included in a finite element method to simulate two plate bonded with bolts. VII. CKNOWLEDGMENT upport of National cience Foundation #CM-9466, hih- Chi Liu, Program Director and Office of Naval Research #N4---7, Dr. Ignacio Perez Program Monitor; are thanfully acnowledged. Copyright by ME
VIII. REFERENCE [] Lamb, H., On waves in an elastic plate Proc. R. oc. London., 97: p. 44-8. [] Rose, J.L., Ultrasonic waves in solid media. Cambridge University Press, 999. [3] Vitorov, I.., Rayleigh and Lamb waves - Physical theory and application. New Yor Plenum Press, 967. [4] chenbach, J.D., Wave propagation in Elastic olids. Elsevier, 973. [] Dieulesaint, E. and Royer, D. Ondes élastiques dans les solides- Tome : Propagation libre et guidée. 996, Paris: Masson. [6] Harer,.H., Elastic waves in solids. 987, Bristol: British gas. [7] Grondel,., et al., The propagation of Lamb waves in multilayered plates: phase-velocity measurement. Measurement cience and Technology, 999. (): p. 348-33. [8] Wilcox, P., M. Lowe, and P. Cawley, The effect of dispersion on long-range inspection using ultrasonic guided waves. NDT & E International,. 34(): p. -9. [9] Grahn, T., Lamb wave scattering from a circular partly through-thicness hole in a plate. Wave Motion, 3. 37(): p. 63-8. [] Castaings, M., Contrôle et évaluation non destructifs de matériaux par ondes ultrasonores guidées., Université Bordeaux. [] Wang, X., Y. Lu, and J. Tang, Damage detection using piezoelectric transducers and the Lamb wave approach: I. ystem analysis. mart materials and structures, 8. 7(): p. 33. [] Lu, Y., et al., Quantitative assessment of through-thicness crac size based on Lamb wave scattering in aluminium plates. NDT & E International, 8. 4(): p. 9-68. [3] Liu, W. and V. Giurgiutiu, Finite Element imulation of Piezoelectric Wafer ctive ensors for tructural Health Monitoring with Coupled-Filed Elements. 7. [4] Za,., M. Krawczu, and W. Ostachowicz, Propagation of in-plane waves in an isotropic panel with a crac. Finite Elements in nalysis and Design, 6. 4(): p. 99-94. [] Greve, D.W., P. Zheng, and I.J. Oppenheim, The transition from Lamb waves to longitudinal waves in plates. mart materials and structures, 8. 7(3): p. 39. [6] ejin Han, C., ROK, Finite element analysis of lamb waves acting within a thin aluminium plate, in Department of eronautical and stronautical Engineering. 7, ir Force Institute of Technology. [7] Yang, Y. and Y. Hu, Electromechanical impedance modeling of PZT transducers for health monitoring of cylindrical shell structures. mart materials and structures, 8. 7(): p.. [8] Giurgiutiu, V., ed. tructural Health monitoring with piezoelectric wafer active sensor. 8, Elsevier Inc. [9] Doyle, D., et al., Damage Detection in Bolted pace tuctures. Journal of intelligent material systems and structure,.. [] Reynolds, W., et al. Wave Propagation in Rib-tiffned tructures: Modeling and Experiements. in Conference on mart Materials, daptive tructures and Intelligent ystems.. Philadelphia, Pennsylvania, U. [] Lin, B and Giurgiutiu, V. Modeling of Power and Energy Transduction of Embedded Piezoelectric Wafer ctive ensors for tructural Health Monitoring, in PIE. : an Diego, C, U. [] Lin, B. and Giurgiutiu, V., implified D modeling of power and energy transduction of piezoelectric wafer active sensors for structural health monitoring. in PIE.. an Diego, C, U. Figure : Comparison between analytical, FEM, and experimental signal receive from a PW (- Hz frequency excitation). 6 Copyright by ME
Normalized magnitude Normalized magnitude c g (m/s) Lamb wave group velocity of luminum-66 6 anti-symmetric symmetric 4 3 4 6 8 f(hz) Figure : Dispersion curve for 3-mm thic aluminum 66-T6 plate. T-PW R- R-PW Rib 4 Rib Rib 6 Figure 3: D geometry used in finite element modeling with sensors. Rib 7.8.6 Receiver at mm.8.6 plate Rib-stiffined Receiver at mm.4.4.. -. -. -.4 -.6 -.8 plate Rib-stiffined - 3 4 6 x - 3 4 6 x - Figure 4: Influence of ribs on sensor signals R-PW at mm from T-PW; R-PW at mm from T-PW. -.4 -.6 -.8-7 Copyright by ME
Normalized magnitude Normalized magnitude. mm x. mm Figure : Modeling of corner crac at rib : FEM mesh geometry; Zoom-in showing densified mesh around crac. receiver at mm receiver at mm.8 pristine crac.8 pristine crac.6.6.4. -. -.4 -.6 -.8-3 4 6 x - 3 4 6 x - Figure 6: FEM prediction of the influence of corner crac on sensor signal; R-PW at mm from T-PW; R-PW at mm from T-PW..4. -. -.4 -.6 -.8 - R-PW R-PW Craced -hole Crac T-PW (c) Figure 7: 3D isogrid model 3D view of the interior; Zoom-in of the exterior view showing the position of the PW transmitter (T) and receiver (R) transducers; (c) Detail of craced hole. 8 Copyright by ME
pristine crac.8.6.6 Normalized magnitude Normalized magnitude pristine crac.8.4. -. -.4.4. -. -.4 -.6 -.6 -.8 -.8-3 4-6 x 3-4 6 x - Figure 8: 3D FEN predictions of the influence of hole crac on sensor signal: R-PW at mm from T-PW; R-PW at ~77 mm from T-PW. Power requirement Excited total wave power Wave Power(mW) Power Rating (mw) frequency (Hz) Transmitter size (mm) Flexural Wave Power(mW) xial Wave Power(mW) Transmitter size (mm) Flexural wave power frequency (Hz) xial wave power frequency (Hz) 6 4 frequency (Hz) Transmitter size (mm) Transmitter size (mm) (c) (d) Figure 9: PW transmitter under constant voltage excitation power rating; wave power; (c) axial wave power; (d) flexural power 9 Copyright by ME
Receiver RM power Transmitter Input Transmitter PW, l=a (Wave Exciter) V Lamb waves Piezoelectric transduction: Elec. Mech. hear-stress excitation of structure Receiver PW (Wave Detector) V B PW-structure interaction Ultrasonic guided waves from transmitter PW tructural function transfer Ultrasonic guided waves arrive at receiver PW Receiver Output Piezoelectric transduction: Mech. Elec. hear-stress excitation of PW tructure-pw interaction Figure : Power and energy flow in a PW pitch-catch configuration..8.6.4. center frequency(hz), rs (-mm) mm mm mm mm 3mm 3mm 4mm 4mm mm x -4 3 3 4 Time (microsecond) Distance (mm) Figure : Pitch-catch signal with a receiver PW at different distance from a transmitter PW, RM power of a receiver at different distance. Copyright by ME