Tuning of Thickness Mode Electromechanical Impedance and Quasi- Rayleigh Wave in Thick Structures

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1 Tuning of Thickness Mode Electromechanical Impedance and Quasi- Rayleigh Wave in Thick Structures Tuncay Kamas, Victor Giurgiutiu, Bin Lin Mechanical Engineering Department, University of South Carolina, Columbia, SC, USA

2 Tuning of Thickness Mode Electromechanical Impedance and Quasi- Rayleigh Wave in Thick Structures This paper discusses theoretical and experimental analyses of thickness-mode electromechanical impedance spectroscopy (EMIS) in regards with the quasi- Rayleigh surface acoustic wave tuning in thick structures. Thickness-mode EMIS and guided wave propagation (GWP) tests have been performed by using piezoelectric wafer active sensors (PWAS). To develop an ultrasonic technique for in-situ structural inspection of thick structure, PWAS has recently been utilized as both resonator for local modal sensing and transducer for far-field interrogation. For latter purpose, PWAS transducers have been employed to carry out pitch-catch technique by transduction of guided ultrasonic elastic waves in solid structures. For single wave mode interpretation, the wave modes are required to be tuned by rejecting undesired modes. Therefore, in this study, quasi-rayleigh waves (QRW), in thick structures are tuned. The tuning effects of the thickness of substrate structure and features on the structure are discussed regarding both EMIS and GWP techniques. The development of QRW mode tuning is performed by analytical and experimental analyses of aluminium and steel specimens. The significant usage of the tuned -QRW mode is essentially discussed for the applications in the in-situ inspection of relatively thick structures such as naval offshore structures. The paper ends with summary and conclusions. Keywords: Thickness-mode; electromechanical impedance; quasi-rayleigh wave; thick structures; ultrasonic wave tuning Introduction Piezoelectric wafer active sensor (PWAS) is light-weighted, inexpensive, unobtrusive, minimally intrusive sensor requiring low-power (Giurgiutiu, Bao, & Zhao, 2001). PWAS is made of piezoelectric ceramic with electric field polarization across the electrodes deposited on both surfaces. It has recently been extensively employed in many applications for in-situ structural inspection in fields such as structural health monitoring (SHM) and non-destructive evaluations (NDE) of aero-structures, nuclear

3 plants, pipelines, pressure vessels, naval offshore structures and so forth. The SHM methods include techniques through guided wave generation/transduction and electromechanical impedance spectroscopy (EMIS). EMIS techniques where PWAS is employed as a resonator are used to generate standing waves in local field of a substrate structure. EMIS method has been utilized to determine the local dynamic characteristics of PWAS bonded on a host structure for insitu ultrasonics. Liang, Sun, & Rogers (1994); Zagrai & Giurgiutiu (2001) utilized the EMIS method for high frequency local modal sensing. EMIS data can be mainly acquired in two modes: in-plane mode and out-of-plane (thickness) mode. The analytical in-plane impedance for piezoelectric ceramic transducers such as PWAS has been developed by Zagrai & Giurgiutiu (2001). One and two dimensional in-plane E/M impedance models for free PWAS and constrained PWAS were derived to model the dynamics of PWAS and substrate structure in terms of EMIS. They assumed the constant electric field E 3 to derive the in-plane EMIS. One and two dimensional inplane E/M impedance models for free PWAS and constrained PWAS were derived to model the dynamics of PWAS and substrate structure in terms of EMIS. They assumed the constant electric field to derive the in-plane EMIS. Another EMIS modelling of PZT actuator-driven active structures is carried out by Liang, Sun, & Rogers (1996) in low frequency range up to 650 Hz in in-plane mode. Park (2014) analytically investigated the EMIS of piezoelectric transducers bonded on a finite beam from the perspective of wave propagation. The analytic solutions of flexural waves are derived for coupled PWAS-infinite beam. Then the concept is used for finite beam in relatively low frequency range. Annamdas & Radhika (2013) also derived E/M admittance model for PWAS bonded on metallic and non-metallic host structures in relatively frequency range up to 500 khz. Park et al. (2003) used the impedance based health monitoring to

4 interrogate a bolt jointed pipeline system in range up to 100 khz and they also monitored the curing process of concrete structures un range between 100kHz-140kHz. Many other researchers have recently applied in-plane EMIS method for dynamically monitoring the smart structures in different materials and forms (Annamdas et al. 2013; Brus, 2013; C. Liang, Sun, 1994; Cheng & Wang, 2001; Parket al. 2012; Pavelko, 2014; Peairs et al., 2003; Almeida, Baptista, & Aguiar, 2014; Rugina et al. 2014; ). Tiersten (1963) presented a pioneering work to develop the analytical solution for the thickness vibration of an anisotropic piezoelectric plate. He used the resonator theory with traction-free T 0 boundary conditions at surfaces of a plate. For high frequency-band in range of MHz, the analytical study for thickness mode of PWAS-EMIS was performed by Kamas, Lin, & Giurgiutiu (2013). They later aimed to extend the analytical thickness-mode EMIS model of a constrained PWAS for high frequencies (up to 15MHz) ( Kamas Giurgiutiu & Lin, 2013a, 2013b, 2014a, 2014b). The authors utilized the constant electric displacement assumption (IEEE Ultrasonics, 1987; Meeker, 1972) and solved the piezoelectric constitutive equations for the thickness mode. Wave direction Rayleigh wave Fig. 1 Waveform of Rayleigh wave on a surface of semi-infinite elastic medium (Reproduced from Rayleigh waves (Fig. 1) are widely used in non-destructive testing (NDT) and SHM applications. Rayleigh wave that resembles to axial wave mode is an elastic wave that propagates close to free surface with as low penetration into the medium as of the order of its wavelength. Rayleigh waves i.e. surface acoustic waves (SAW) are a high

5 frequency approximation of the S0 and A0 Lamb waves as the frequency becomes relatively high. They become non-dispersive wave, i.e. constant wave-speed along the frequency. It can be seen in dispersion curves of Lamb wave modes (Fig. 4) that for large frequency-thickness products, the wave speeds of A 0 and S 0 Lamb wave modes coalesce at the wave speed of a Rayleigh wave. Rayleigh wave can only travel along a flat surface of a semi-infinite medium, which is hardly possible to generate in reality however for the plate thickness d>>λ R, the measurements should be acceptable(brook, 2012). The wave mode is then called quasi-rayleigh wave (QRW) having Rayleigh wave speed. QRW in an isotropic elastic medium are in many cases an appropriate tool for ultrasonic inspection by utilizing the useful property of Rayleigh waves, the propagation speed is independent of frequency (Cook & Berthelot, 2001). In the literature, the QRW as known as SAW or surface guided wave has been utilized for insitu monitoring of many types of defects in a medium. (Chew & Fromme, 2014; Fromme, 2013; Masserey & Fromme, 2014) used Rayleigh waves for detection of fatigue crack growth and corrosion through wall thickness with theoretical predictions for the thickness loss. The tuned QRW mode is of paramount importance for the applications in the in-situ inspection of relatively thick structures such as thick walls of nuclear power plants or naval offshore structures (Kamas, Giurgiutiu & Lin, 2014). In the current study, one dimensional analytical thickness mode EMIS model for PWAS constrained on a host structure is presented. The analytical constrained PWAS- EMIS results in relatively high frequency range are analysed regarding the clarity of the trend, easy predictability of the experimental impedance spectra and decent agreement between experimental and analytical E/M impedance spectra by relating the dominant QRW mode tuned in high frequency band and in thick structures. Therefore, one can obtain adequate impedance prediction by the axial wave approximation in the Rayleigh

6 wave region since Rayleigh wave is a non-dispersive i.e. wave speed is independent from frequency alike axial waves. Thickness of the substrate is significant parameter to adjust the thickness mode resonance frequency band where SAW mode are tuned up by using the proof-mass concept of the fact that proof-masses shift system resonance towards optimal frequency point. In a recent study, proof-mass PWAS (PM-PWAS) resonator is introduced (Kamas, Lin, & Giurgiutiu, 2014) and analytical and numerical simulations are presented for different thickness of proof-masses bonded on PWAS resonators to study the phenomenon of increasing proof-mass height shifts the local system resonance downward. Kamas et al. (2014) discussed the tuning effect of the change in thickness of the substrate material on standing wave modes in local sensing and guided wave modes regarding especially tuned and guided QRW mode propagating in the structure with various feature and thickness. The current paper also discusses QRW tuning curves calculated analytically in terms of strain and measured experimentally in terms of the ratio of the output to input voltage. The tuning curves are determined to show the tuning effect of the structure thickness on producing a dominant QRW mode. Constrained PWAS-EMIS Fig. 2 One dimensional model of a two layer resonator model including a PWAS constrained by an isotropic elastic bar.

7 The thickness mode impedance model shown in Eq. (1) has been developed by Kamas et-al. (2014) for constrained PWAS (Fig. 2) by using the resonator theory under constrained boundary conditions and constant electrical displacement, D 3, assumption. As following the procedure shown in the flow-chart in Fig. 3, the frequency response function (FRF) expression was determined through the normal mode expansion (NME) method and the inverse of the FRF gave the dynamic structural stiffness k ( ) that was substituted into the thickness mode EMIS equation for constrained PWAS by the D stiffness ratio, r( ) k ( ) / k where k Ac / 33 t and A is the PWAS surface str PWAS D area, c 33 the stiffness, and t the thickness, the superscript denotes the constant electric displacement assumption. PWAS str V Z 1 33 I i C 0 tcot t r (1) where the E/M impedance is the ratio of the voltage V to the current I, and in terms of the angular frequency, the capacitance C 0, the E/M coupling coefficient 33 in 1 D thickness mode, and t t/ ct is the function of the wave number, c 33 2 / t c is D the phase velocity of axial wave and c 33 is the stiffness (elastic modulus) in thickness direction, is the mass density of the piezoelectric material which generates the standing axial wave in local of the substrate structure where PWAS is situated.

8 Fig. 3 Flow chart of the 1-D analytical thickness mode EMIS for PMPWAS For the analytical simulations of thickness mode EMIS of constrained PWAS, A square PWAS in 7mm x 0.2mm dimensions is modeled as a layer on a homogeneous isotropic material (aluminum) substrate layer (Fig. 2). The piezoelectric material properties defined in Table 1 are taken into account to model the PWAS. The substrate material is modelled as an aluminium plate-like structure. The aluminium density is assumed to be 2780 kg/m 3 and the elastic modulus is 72.4 GPa.

9 Quasi-Rayleigh Wave Tuning Curve c/c S Lamb wave phase velocity of Steel-AISI-4340-norm S0 A0 A1 anti-symmetric symmetric S1 Quasi-Rayleigh wave region fd (khz mm) Fig. 4 Phase velocity dispersion curves of fundamental Lamb wave modes: fd is the product of frequency and half thickness of plate Quasi-Rayleigh wave is an elastic wave that propagates close to free surface with as low penetration into the medium as of the order of its wavelength. In this section, by assuming 1-D medium, a solution for the tuning curve of the QRW generated by PWAS ideally bonded on a substrate structure is conducted by using the similarity of QRW to the axial wave. The strain as a function of distance along which the surface guided wave travels was obtained by 0 sin x i ae i( x t) a 0 (2) for harmonic excitation (Giurgiutiu, 2008) where du / dx the strain that is spatial derivative of the displacement in 1-D medium, ˆ a d31e3 is the induced strain that is a product of d 31 the in-plane induced strain coefficient and Ê 3 the amplitude of the induced electrical field between PWAS electrodes. The wave-number 0 / cr is calculated by using the Rayleigh wave speed c R that is calculated by c c S R c E 21 S (3)

10 Mode-Shape Analysis The mode shape analysis is conducted in order to depict the resemblance between mode shapes obtained from the standing wave analysis and the mode shapes acquired from the propagating guided Lamb wave analysis. The mode shapes begin to have this similarity as approaching to the QRW region shown in the phase velocity dispersion curve (Fig. 4). In both standing and guided wave mode shape analyses, the material properties used for PWAS are shown in Error! Reference source not found.. The model used in standing wave mode shape analysis is schematically illustrated in Fig. 5(a) and the model used in the guided wave mode shape analysis is also depicted in Fig. 6. The density of aluminium substrate is assumed to be 2780 kg/m 3 and the elastic modulus is 72 GPa. The plate thickness is 2.1 mm and the PWAS thickness is 0.2mm. The PWAS is assumed to be 7mmx7mm square in both mode shape analyses. The mode shapes from both analyses are presented at the same resonance frequencies in this study. The thickness mode resonance frequencies are respectively 1.19 MHz, 2.49 MHz, and 3.85 MHz. Table 1 SM412 (PZT-5A) Piezoelectric material properties

11 Standing wave mode shape analysis The standing wave analysis uses the axial wave approximation across the thickness of PWAS and the aluminium plate-like structure that hosts the PWAS. The mode shapes at certain thickness mode resonance frequencies are shown in Fig. 5(b). y (a) (b) E 3 E,, u, s, d p p p E PWAS E,, u a a a Aluminum substrate x 1.19 MHz 2.49 MHz 3.85 MHz Fig. 5 (a) Schema of PWAS transducer ideally bonded on aluminum plate and (b) high frequency modal analysis results considering the standing waves in thickness mode for PWAS bonded on aluminum plate: plate thickness=2.1 mm, PWAS thickness=0.2mm.

12 Guided wave mode shape analysis The guided wave analysis uses the Lamb wave (superposition of axial and flexural wave approximation) propagating in a plate. The mode shapes across the thickness of the aluminium plate structure are simulated. The mode shapes at certain thickness mode resonance frequencies are shown in Fig. 7. PWAS Lamb waves Plate Fig. 6 Schema of PWAS transducer ideally bonded on aluminum plate 1.19 MHz 2.49 MHz 3.85 MHz Fig. 7 High frequency modal analysis results considering the guided waves in thickness mode for PWAS bonded on aluminum plate: plate thickness = 2.1 mm, PWASthickness=0.2mm. As considering the mode shapes from both standing and guided wave analysis, the similarity between the first standing axial wave mode shape and the S0 mode shape is obvious because the S0 mode is non-dispersive alike axial wave at 1.19 MHz.

13 However, the similarity occurs at 2.49 MHz between the second thickness mode shape and the A0 mode since A0 mode is predominant having much higher displacement amplitude than that of S0 mode. A0 mode also becomes non-dispersive as the structure is excited at the second resonance frequency. At the third thickness mode, since A0 is predominant and non-dispersive, the resemblance still occurs between the A0 mode shape and the third thickness mode shape. The aluminium plate is actually excited in the QRW region as the excitation frequencies are at the second and third thickness mode resonance frequencies. Experiments In the experiments, 7mm x 7mm x 0.2mm PWAS transducers are bonded on the specimens. PWAS transducers served as high-bandwidth strain sensors for active sensing of local and far-field in the substrate structures. EMIS and GWP tests have been conducted on thick isotropic elastic specimens such as aluminium and steel plates by using SM412 PWAS transducers on each substrate material. In order to discuss the tuning effect of the thickness of the thick plate-like structures in relatively high frequency region, and the tuning effect of a feature on the structures, the EMIS tests and the experimental tuning curve measurements have been conducted. The results from the analytical models and the tests are compared to discuss the tuning of QRW mode that can be excited in thick structures and at high frequencies. Clear and smooth trend observed in the spectra in frequency domain as the QRW is locally excited and distinguishability of the dominating the QRW packet in time domain. These features of the QRW are promising features that ease the predictability and the signal postprocessing.

14 Electromechanical Impedance Spectroscopy The E/M impedance SHM method is direct and convenient to implement, the only required equipment being an electrical impedance analyser, such as HP 4194A impedance analyser. A HP 4194A impedance analyser was used for the experimental analysis. The impedance analyser reads the E/M impedance of PWAS itself as well as the in-situ E/M impedance of PWAS attached to a specimen. It is applied by scanning a predetermined frequency range in high frequency band (up to 15MHz) and recording the complex impedance spectrum. A LabView data acquisition program was used to control the impedance analyser and sweep the frequency range in steps that was predefined and to attain the data in a format that assists to data analysis. During the visualization of the frequency sweep, the real part of the E/M impedance Z follows up and down variation as the structural impedance goes through the peaks and valleys of the structural resonances and anti-resonances. Electro-mechanical impedance spectroscopy (EMIS) method has been utilized to determine the local dynamic characteristics of PWAS bonded on a host structure for insitu ultrasonics structural monitoring. Thickness mode EMIS of constrained PWAS was analytically simulated and compared with the results from experimental analyses of two relatively thick aluminium specimens. In the EMIS experimental setup, two pristine aluminium specimens are used. PWAS transducers are bonded on the short edges and clays are applied on long edges of the both aluminium specimens to avoid reflections and obtain more clear signals. One PWAS is bonded at centre location of 2.1 mm thick plate shown in Fig. 8 whereas other two PWAS transducers are bonded on the two ends of the 6.35 mm (1/4 in.) thick plate (Fig. 9) in order to avoid the possible reflections from the non-clayed edges. The two

15 PWAS transducers are employed as resonators for EMIS measurements; and transmitter PWAS (T-PWAS) and receiver PWAS (R-PWAS) for pitch-catch tests later on. 7x7mm 2 PWAS Fig. 8 Square PWAS in 0.2mm thickness bonded on a pristine aluminium plate in 2.1mm thickness. T-PWAS R-PWAS Fig. 9 Two square PWAS transducers in 0.2mm thickness are bonded on a pristine aluminium plate in ¼ thickness. Guided Wave Propagation with Pitch-Catch Method PC Arbitrary waveform function generator Transmitter (Wave Exciter) V 1 V 2 Receiver (Wave Detector) Digital Oscilloscope Fig. 10 Schematic of a PWAS pitch-catch setup on a bar. In this experimental setup, transmitter PWAS bonded on a substrate structure excites the structure by induced voltage in tone-burst sine wave form with three-counts through the function generator. Then, receiver PWAS senses the wave signals traveling in certain modes along the structure and the received signals as output voltage are read by the oscilloscope in time domain and recorded for post-processing the data. The pitch-catch tests have been conducted in both the thick section aluminium specimen shown in Fig. 9

16 and the thick steel specimen shown in Fig. 11. The steel specimen is mm thick high temperature steel that has V-groove butt weld bead lying along the centre of the plate. The weld bead is around 1mm thicker than the steel plate and ground flush. The welded thick steel plate specimen was produced using metal inert gas (MIG) welding and provided by Savannah River Nuclear Plant. In this particular study, we were interested in QRW mode, therefore we selected relatively high excitation frequency band to receive the signal dominated by QRW modes. R-PWAS T-PWAS PWAS 1 Weld bead PWAS 2 PWAS 3 Fig. 11 A pristine butt-welded steel plate in sizes of 460mmx460mmx14mm. Auto-tuning graphical user interface (GUI) -developed in LAMSS using LabView programme- was utilized to control the function generator and automatically sweep the predefined frequency band and record the data for each frequency step in an excel file then eventually post-processed the data to generate the tuning curve for certain wave packets in the received signals. EMIS Results and Discussion In this section, the analytical prediction of thickness mode EMIS and the experimental EMIS measurements are compared for the two aluminium specimens that are defined in

17 ReZ, Ohms the preceding section regarding the experiment EMIS setup. Fig. 12 indicates the comparison between the analytical and experimental results for the real part of impedance; dotted line shows the test results and continuous line depicts the thickness mode analytical prediction for the large aluminium specimen in thickness of 2.1mm X: 2.43 Y: X: 3.66 Y: Analytical and Experimental EMIS X: 5.07 Y: X: Y: X: Y: X: 6.51 Y: Analytical Experimental X: Y: X: Y: X: 8 Y: X: Y: Frequency, MHz Fig. 12 Constrained PWAS-EMIS measurement and 1-D analytical prediction to indicate real part of the impedance spectra in thickness mode. Fig. 13 illustrates another thickness mode EMIS comparison for PWAS bonded on the 1/4 thick aluminium specimen. The upper plot shows the analytical prediction whereas the lower plot demonstrates the experimental impedance measurements for both the transmitter PWAS and the receiver PWAS that are installed along the nonclayed edges of the aluminium plate. The constrained PWAS-EMIS measurements somewhat collided that shows the consistency of the experimental setup. The two comparisons of the EMIS results for the two aluminium specimens indicates decent agreement in terms of the anti-resonance frequency and the number of the impedance peaks in the thickness mode EMIS prediction of constrained PWAS and the corresponding experimental measurements. The agreement still occurs even at higher harmonic thickness mode overtones. The analytical prediction in thickness mode possesses the axial wave approximation that is non-dispersive mode alike guided QRW mode in relatively thick structures. The smooth trends that QRW packet follows over

18 relatively high frequency band and distinctive and predominant QRW packets among other wave packets in the received signal were observed. These are promising features that eases predictability and signal processing. As the thicker specimens are analysed, it s realized that the frequency band where QRW packets can be excited becomes lower. Therefore, it gives the advantage of having the QRW mode in also local thickness mode modal sensing because thickness mode EMIS is also for relatively high frequency range in order of MHz. Since QRW resembles to the axial wave which has constant wave speed with respect to frequency as seen in the dispersion plot in Fig. 4, prediction of the E/M impedance signature of the local structure in thickness mode becomes easier. One can use the proof-mass concept by increasing the thickness or density of the substrate analysed to attain QRW mode and downshift the local resonance frequency of PWASsubstrate structure so that the thickness mode constrained PWAS-EMIS signature becomes easily predictable by using the standing QRW mode in local structural dynamic sensing

19 ReZ, Ohm ReZ, Ohms (a) (b) ReZ, Ohms ReZ, Ohms 1-D Analytical Bonded PWAS Impedance 10 X: X: Y: Y: Frequency, MHz X: Y: X: 1.44 Y: X: Y: X: Y: X: Y: Experimental Bonded Square-PWAS Impedance Result X: Y: X: Y: X: Y: X: Y: X: Y: X: Y: X: Y: X: Y: X: 3.73 Y: X: Y: X: 4.68 Y: X: Y: T-PWAS R-PWAS X: Y: Frequency, MHz Fig. 13 (a) Analytical and (b) experimental thickness mode EMIS results for 7x7 mm 2 square PWAS bonded on ¼ thick aluminium plate.

20 Amplitude, mv GWP Signals and QRW Tuning Curves Received signal on aluminum plate F c =300 khz Quasi-Rayleigh wave F c =360 khz F c =480 khz F c =600 khz Time, µs Fig. 14 Received signals from 7x7 mm 2 PWAS on ¼ thick aluminum plate at different frequencies GWP test has also been conducted on the ¼ thick aluminum specimen using the PWAS transducers as transmitter and receiver in this task. Tone-burst sine wave with 3 counts is generated through the function generator to excite the transmitter PWAS and generate a strain wave into the host aluminium plate. The guided wave information travels in the material in different modes and at various wave speeds depending on the excitation frequency-thickness product. In this particular study, we are interested in QRW mode, therefore we selected relatively high excitation frequency band to receive the signal dominated by guided QRW modes as can be seen in a few examples of received QRW signals (Fig. 14) that travels at constant wave speed i.e. independent from frequency change. The all received wave signals show that QRW packet appears

21 distinctly dominating among other wave packets at the same time window eventhough the frequency increases in the range between 300 khz and 600 khz as seen in Fig. 14. The experimental tuning curve in terms of input/output voltage ratio was obtained. The tuning curve in the frequency band between khz is illustrated in Fig. 15. The upper plot shows the analytical calculation of QRW tuning curve whereas the lower plot shows the experimental reading of the tuning curve. For the analytical prediction of the QRW tuning curve in terms of strain amplitude, the induced strain a d31e3 was calculated by the product of the piezoelectric constant d 31 and the electric field E 3 V / t. The piezoelectric constant was -190x10-12 m/v as given value in Table 1 and the electric field was 100 kv/m where the input voltage V was assumed to be 20 V and the PWAS thickness t was 0.2 mm. The density of aluminium plate was 2780 kg/m 3 whereas the elastic modulus E was 72.4 GPa and the distance between the PWAS transducers are 910 mm. Eventually, harmonic sinusoidal tuning curve for QRW mode was obtained Fig. 15(a). The calculated QRW phase velocity in the aluminum plate was found to be 2657 m/s. The analytical and experimental QRW phase velocity results for the ¼ thick aluminum specimen were also obtained and compared as seen in Fig. 16(a) with decent agreement. The trends that the analytical and experimental tuning curves follow agree somewhat closely. They possess the valleys and hills appear in the fairly close frequency bands as can be seen in Fig. 15.

22 (a) (b) Fig. 15 (a) Analytical simulation (b) experimental measurement of tuning curves of quasi-rayleigh wave from pitch-catch in an aluminum plate in thickness of 1/4 and the distance between the PWAS transducers are 910 mm. The density of the butt welded thick steel plate was 7850 kg/m 3 whereas the elastic modulus E was 210 GPa and the distance between the PWAS transducers are 460 mm. Eventually, harmonic sinusoidal tuning curve for QRW mode was analytically obtained as shown in Fig. 17(a). The calculated QRW phase velocity in the aluminum plate was found to be 3103 m/s. The analytical and experimental QRW phase velocity results for the steel specimen were also obtained and compared as seen in Fig. 16(b) with decent agreement.

23 c R m/s c R m/s (a) Rayleigh wave phase velocity Experimental Calculated (b) Rayleigh wave phase velocity Experimental Calculated Frequency, khz f(khz) Fig. 16 Comparison between the experimental and calculated values of the QRW phase velocity in wide frequency-band for (a) ¼ thick aluminium plate and (b) 14mm thick steel plate (a) (b) (c) Fig. 17 (a) Analytical simulation (b) experimental measurements of tuning curves of quasi-rayleigh wave from pitch-catch in a butt welded steel plate in thickness of 14mm across weld bead (c) along weld bead and the distance between the PWAS transducers are 460 mm

24 The trends that the analytical tuning curve simulation Fig. 15(a) and the experimental tuning curves of quasi-rayleigh wave from pitch-catch across the weld bead Fig. 15(b) follow agree somewhat closely. They possess the valleys and hills appear in the fairly close frequency bands. However, the trend of the experimental tuning curve of QRW from pitch-catch along the weld bead Fig. 15(c) was different. This difference was presumed to be due to the existence of the weld bead that varies the QRW mode tuning. The weld bead fosters the amplitude of the QRW that travels along the weld bead for wider frequency band as observed in Fig. 15(c). Summary and Conclusions Electro-mechanical impedance spectroscopy (EMIS) method has been utilized to determine the local dynamic characteristics of PWAS bonded on a host structure for insitu ultrasonics. Thickness mode EMIS of constrained PWAS was analytically simulated and validated using results from experimental analysis of two aluminium specimens. GWP test has also been conducted on two isotropic elastic specimens such as thick aluminium and steel plates by using two SM412 PWAS transducers on each substrate material as transmitter and receiver. In this particular study, we are interested in quasi-rayleigh wave mode, therefore we selected relatively high excitation frequency band to receive the signal dominated by QRW modes. QRW in an isotropic elastic medium are in many cases an appropriate tool for ultrasonic inspection by utilizing the useful property of QRW, the propagation speed is independent of frequency QRW trend over frequency and distinguishability of dominating wave packet are promising features that eases predictability and signal processing. The thicker and heavier specimens are analysed, the higher frequency band where Rayleigh wave packets appear is observed. Therefore, it gives the advantage of having the Rayleigh

25 wave mode as a standing wave in also local thickness mode modal sensing because thickness mode EMIS is also for relatively high frequency range in order of MHz. Since the dominating Rayleigh wave resembles to the axial wave which has constant wave speed with respect to frequency as seen in the dispersion plot in Error! Reference source not found., prediction of the E/M impedance signature of the local structure in thickness mode becomes easier. As seen in the dispersion curves for PWAS ideally bonded on steel substrate, other wave modes such as first symmetric (S 0 ) and antisymmetric (A 0 ) Lamb wave modes do not interfere as much as Rayleigh wave mode as also obvious in the received signals (Error! Reference source not found. and Error! Reference source not found.) in certain frequency band; One can use the proof-mass concept by increasing the thickness or density of the substrate analysed to attain Rayleigh wave mode and downshift the local resonance frequency of PWAS-substrate structure so that the thickness mode constrained PWAS- EMIS signature becomes easily predictable by using the standing Rayleigh waves in local structural dynamic sensing For the GWP test in the butt-welded steel plate, the analytical tuning curve simulation for the QRW mode that travel in a pristine plane plate was performed. The analytical and the experimental tuning curve of QRW from pitch-catch across the weld bead agree somewhat. They possess the valleys and hills appear in the fairly close frequency bands. However, the experimental tuning curve of QRW from pitch-catch along the weld bead was varied due to the wave trapped by the weld bead that varies the QRW mode tuning. The weld bead was presumed to contribute to the amplitude of the QRW that travels along the weld bead for wider frequency band.

26 Acknowledgments Support from National Science Foundation Grant # CMS ; Office of Naval Research #N , Dr. Ignacio Perez, Program Manager; are thankfully acknowledged. References Annamdas, V. G., Pang, J. H., Zhou, K., & Song, B. (2013). Efficiency of electromechanical impedance for load and damage assessment along the thickness of lead zirconate titanate transducers in structural monitoring. Journal of Intelligent Material Systems and Structures, 24(16), doi: / x Annamdas, V. G., & Radhika, M. a. (2013). Electromechanical impedance of piezoelectric transducers for monitoring metallic and non-metallic structures: A review of wired, wireless and energy-harvesting methods. Journal of Intelligent Material Systems and Structures, 24(9), doi: / x Brook, M. V. (2012). Ultrasonic Inspection Technology Development and Search Unit Design: Examples of Pratical Applications (p. 216). IEEE press. Retrieved from =rayleigh+waves+in+thick+plates&source=bl&ots=r15k6jlyj9&sig=nmfabahq ZK_bvnCarJgpA- 4pFY0&hl=tr&sa=X&ei=NUDFU6DkEsTIsATfhYKwBg&ved=0CF8Q6AEwBg #v=onepage&q=rayleigh waves in thick plates&f=false Brus, V. V. (2013). The effect of interface state continuum on the impedance spectroscopy of semiconductor heterojunctions. Semiconductor Science and Technology, 28(2), doi: / /28/2/ C. Liang, F. P. Sun, C. A. R. (1994). An impedance method for dynamic analysis of active material systems. Journal of Vibration and Acoustics, 116(1), Retrieved from &TokenID=wnOfoYHMIYjHr28oNxcKd8pcGbVO27Dm6u2QrcJm6j1x55a LUrwGAeDpSSK3oy9g Cheng, C. C., & Wang, P. W. (2001). Applications of the Impedance Method on Multiple Piezoelectric Actuators Driven Structures. Journal of Vibration and Acoustics, 123(2), 262. doi: / Chew, D., & Fromme, P. (2014). Monitoring of corrosion damage using high-frequency guided ultrasonic waves, 9064, 90642F. doi: / Cook, D. A., & Berthelot, Y. H. (2001). Detection of small surface-breaking fatigue cracks in steel using scattering of Rayleigh waves, 34, Dare de Almeida, V., Baptista, F., & Roberto de Aguiar, P. (2014). Piezoelectric Transducers Assessed by the Pencil Lead Break for Impedance-Based Structural Health Monitoring. IEEE Sensors Journal, (c), 1 1. doi: /jsen Fromme, P. (2013). Noncontact measurement of guided ultrasonic wave scattering for fatigue crack characterization, 8692, 86921N. doi: / Giurgiutiu, V. (2008). Structural Health Monitoring with Piezoelectric Wafer Active Sensors. Columbia, SC, USA.

27 Giurgiutiu, V., Bao, J., & Zhao, W. (2001). Active Sensor Wave Propagation Health Monitoring of Beam and Plate Structures. In Proc of SPIE s 8th International Symposium on Smart Structures and Materials. Newport Beach, CA. IEEE Ultrasonics. (1987). IEEE Standard on Piezoelectricity. New York, New York, USA: The institute of Electrical and Electronics Engineers, Inc. Kamas, A. T., Giurgiutiu, V., & Lin, B. (2013). Analytical Modeling of Proof-Mass Piezoelectric Wafer Active Sensor for Symmetric Lamb Waves Tuning. In International workshop of Structural Health Monitoring, IWSHM. San Francisco, CA. Kamas, T. (2012). Carbon Resistivity Conductivity and Capacitance Measurement under Various Pressure. Kamas, T., Giurgiutiu, V., & Lin, B. (2014a). Modeling and Experimentation of Thickness Mode E/M Impedance and Rayleigh wave Propagation for Piezoelectric Wafer Active Sensors on Thick Plates. In ASME-SMASIS (pp. 1 9). Kamas, T., Giurgiutiu, V., & Lin, B. (2014b). Thickness Mode EMIS of Constrained Proof - Mass Piezoelectric Wafer Active Sensor. Smart Structures and Systems, Kamas, T., & Lin, B. (2014). Quasi-Rayleigh Waves in Butt-Welded Thick Steel Plate. In AIP Conference Proceedings: Quantitative Nondestructive Evaluation. Kamas, T., Lin, B., & Giurgiutiu, V. (2013). Analytical modeling of PWAS in-plane and out-of-plane electro- mechanical impedance spectroscopy ( EMIS ). In SPIE Smart Structure and Materials + Nondestructive Evaluation and Health Monitoring 2013, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. Kamas, T., Lin, B., & Giurgiutiu, V. (2014). Modeling and Experimentation of Proof- Mass Piezoelectric Wafer Active Sensor Thickness Mode E/M Impedance Spectroscopy. In AIAA Region II Student Conference (pp. 1 12). Memphis, TN. Liang, C., Sun, F. P., & Rogers, C. a. (1994). Coupled Electro-Mechanical Analysis of Adaptive Material Systems -- Determination of the Actuator Power Consumption and System Energy Transfer. Journal of Intelligent Material Systems and Structures, 5(1), doi: / x Liang, C., Sun, F., & Rogers, C. a. (1996). Electro-mechanical impedance modeling of active material systems. Smart Materials and Structures, 5(2), doi: / /5/2/006 Masserey, B., & Fromme, P. (2014). Noncontact monitoring of fatigue crack growth using high frequency guided waves, 9061, 90611D. doi: / Meeker, T. R. (1972). Thickness mode piezoelectric transducers. Ultrasonics, 10(1), Park, G., Sohn, H., Farrar, C. R., & Inman, D. J. (2003). Overview of Piezoelectric Impedance-Based Health Monitoring and Path Forward. The Shock and Vibration Digest, 35(6), doi: / Park, H. W. (2014). Understanding the electromechanical admittance of piezoelectric transducers collocated on a finite beam from the perspective of wave propagation. Journal of Intelligent Material Systems and Structures. doi: / x Park, H.-J., Sohn, H., Yun, C.-B., Chung, J., & Lee, M. M. S. (2012). Wireless guided wave and impedance measurement using laser and piezoelectric transducers. Smart Materials and Structures, 21(3), doi: / /21/3/035029

28 Pavelko, V. (2014). New applications of a model of electromechanical impedance for SHM. In T. Kundu (Ed.), SPIE Health Monitoring of Structural and Biological Systems (Vol. 9064, p Y). doi: / Peairs, D. M., Grisso, B., Inman, D. J., Page, K. R., Athman, R., & Margasahayam, R. N. (2003). Proof-of-Concept Application of Impedance Based Health Monitoring on Space Shuttle Ground Structures. National Aeronautics and Space Administration. Rugina, C., Giurgiutiu, V., Toader, A., & Ursu, I. (2014). The electromechanical impedance method on thin plates. Sun, F. P., Liang, C., & Rogers, C. A. (1994). Structural modal analysis using collocated piezoelectric actuator/sensors: an electromechanical approach. In Proc. SPIE 2190, Smart Structures and Materials 1994: Smart Structures and Intelligent Systems, 238. Orlando, FL. Tiersten, H. F. (1963). Thickness Vibrations of Piezoelectric Plates. J. Acoustic Society of America, 35(1), Zagrai, A., & Giurgiutiu, V. (2001). Electro-Mechanical Impedance Method for Crack Detection in Thin Plates. Journal of Intelligent Material Systems and Structures, 12(October 2001). Retrieved from Zagrai, A. N., & Giurgiutiu, V. (2001). Electro-Mechanical Impedance Method for Damage Identification in Circular Plates, 40.

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