Ultrasonics 89 (2018) 13–21
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A variable-frequency bidirectional shear horizontal (SH) wave transducer based on dual face-shear (d24) piezoelectric wafers ⁎
T
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Hongchen Miaoa, , Qiang Huanb, Faxin Lib, , Guozheng Kanga a
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China b LTCS and Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Structural health monitoring (SHM) Shear horizontal wave Circumferential guided wave Piezoelectric transducer
Focusing the incident wave beam along a given direction is very useful in guided wave based structural health monitoring (SHM), as it will not only save input power but also simplify the interpretation of signals. Although the fundamental shear horizontal (SH0) wave is of practical importance in SHM due to its non-dispersive characteristics so far there have been very limited transducers which can control the radiation patterns of SH0 wave. In this work, a variable-frequency bidirectional SH0 wave piezoelectric transducer (BSH-PT) is proposed, which consists of two rectangular face-shear (d24) PZT wafers. The opposite face-shear deformation of the two PZT wafers under applied electric fields makes the BSH-PT capable of exciting SH0 wave along two opposite directions (0° and 180°). Both finite element simulations and experimental testings are conducted to examine the performance of the proposed BSH-PT. Results show that pure SH0 wave can be generated by this BSH-PT and its wave beam can be focused bi-directionally. Moreover, the bidirectional characteristics of the BSH-PT can be kept over a wide frequency range from 150 kHz to 250 kHz. As the circumferential SH0 (CSH0) wave in a thin hollow cylindrical structure is essentially equivalent to the SH0 wave in a plate, the proposed BSH-PT may also be very useful to develop a CSH0-wave-based SHM system for hollow cylindrical structures.
1. Introduction Guided wave inspection method has attracted much attention in structural health monitoring (SHM) as it can cover large area of the structure, while the bulk-wave-based method can only detect a localized area just below the transducer [1]. A good guided-wave-based SHM system requires that the signal complexity and consumed power are minimized. To realize such a goal, it is necessary to control the radiation pattern of the incident wave for the following reasons. On one hand, focusing all the incident energy along a given direction will not only save input power but also improve the damage detection resolution of the incident wave. On the other hand, in practical applications, the coherent noise due to spurious signals from reflectors is a serious problem [2]. Controlling the wave directivity can significantly decrease the coherent noise and then simplify the interpretation of signals [3]. In the past decades, various approaches have been adopted to control Lamb wave beams in SHM system which can mainly be classified into three types: phased array [2,4,5], interference based on sizeoptimized transducer [6,7] and surface bonded elastic metamaterials [8]. Using phased array technologies, wave front can be focused at a
⁎
Corresponding authors. E-mail addresses:
[email protected] (H. Miao),
[email protected] (F. Li).
https://doi.org/10.1016/j.ultras.2018.04.010 Received 13 March 2018; Received in revised form 21 April 2018; Accepted 24 April 2018 Available online 24 April 2018 0041-624X/ © 2018 Elsevier B.V. All rights reserved.
target point and steered in a prescribed direction by electronically sweeping [4]. As the electronically sweeping required expensive and complex electronics, the signal post-processing approach [2,5,9] was then proposed to avoid this problem, which realized virtual beam steering. Using destructive and constructive interference conditions, the size of transducers can be optimized to generate bidirectional Lamb wave [6,7]. Interdigital transducers are representative bidirectional Lamb wave transducers based on interference [7,10–12]. The wave beam of bidirectional transducers can be steered if a series of transducers in a phased array form are used, although the individual transducer is unable to steer its wave beam direction. Using surface bonded elastic metamaterials is another method to focus Lamb waves [8]. However, this method requires that the out-of-plane displacement of the wave mode is dominant, thus it is difficult to control symmetric Lamb waves. Compared with Lamb waves, the fundamental shear horizontal (SH0) wave is more attractive for SHM due to its non-dispersive characteristics, which can significantly reduce the complexity of signal interpretation and extend the inspection distance [13,14]. Bidirectional [15,16], unidirectional [17] and beam controllable [18,19] SH0 waves
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Fig. 1. Comparison of the square (up) and rectangular (bottom) face-shear (d24) mode PZT wafer. Left: schematics, where V+ (or V−), P and τ are the applied voltage, polarization and shear stress respectively. λ is the wavelength of SH0 wave and n is a positive integer; Right: finite element simulated tangential displacement (SH0 wave) in the cylindrical coordinate excited by the d24 PZT wafer.
proposed transducer is made up of two rectangular face-shear (d24) PZT wafers. Its configuration and working principle will be presented firstly. Then we demonstrate the bidirectivity of the proposed transducer via finite element simulations. Finally, experiments are performed to investigate the bidirectivity of the SH0 wave generated by the proposed transducer. For convenience, the proposed transducer is referred to as BSH-PT (bidirectional SH0 wave piezoelectric transducer) in subsequent sections.
have been realized by various electromagnetic acoustic transducers (EMATs). Piezoelectric transducers are more attractive for SHM, due to their compact size and peculiar electromechanical coupling properties. However, so far there have been very few piezoelectric transducers which can control the radiation patterns of SH0 wave. Three types of omnidirectional SH0 wave piezoelectric transducers [20–22] have been developed and theoretically they can be used to constitute a phased array system to control the SH0 wave direction, but such a system has not been reported yet. Recently, a size-optimized d15 PZT wafer [23] and a face-shear piezoelectric fiber patch transducer [24] were proposed, both of them can generate bidirectional SH0 wave. However, these two bidirectional transducers usually need narrow band operation. In other words, if the excitation frequency deviates much from the desired frequency, waves in the unwanted direction cannot be eliminated totally, resulting in the degeneration of their bidirectivity. Since the wavelength is related to the sensitivity to damages, a frequency tunable transducer means that it has the tunable detection sensitivity for damages of different sizes. Therefore, it is necessary to develop a bidirectional SH0 wave piezoelectric transducer which can be operated in a wide frequency range without loosing its bidirectivity. In this work, we propose a bidirectional SH0 wave piezoelectric transducer, which is capable of focusing SH0 wave beams in two opposite directions (0° and 180°) over a wide frequency range. The
2. Configuration and working principle of the BSH-PT As indicated in our previous work [25], a square face-shear (d24) PZT wafer shown in Fig. 1(a) will generate SH0 wave along four main directions (0°, 90°, 180° and 270°), as seen in the finite element (FE) simulation shown in Fig. 1(b). In order to excite bidirectional SH0 wave and suppress the waves along other two directions, using a rectangular face-shear (d24) PZT wafer is a straightforward method. As shown in Fig. 1(c), the length of the rectangular d24 PZT wafer is a multiple of the wavelength of SH0 wave, while its width equals to an odd multiple of the half wavelength. Therefore, as shown in the FE simulation in Fig. 1(d), the amplitude of the excited SH0 waves will reach its maxima along the 0° and 180° directions due to the constructive interference, while the amplitude will get the minima along the 90° and 270° 14
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Fig. 2. Schematics of the proposed variable-frequency bidirectional SH0 wave piezoelectric transducer (BSH-PT): (a) Top view, where L and w are the length and width of PZT wafers respectively; (b) 3-D view of a single wafer; (c) Photo; (d) Bidirectional SH0 wave driving mechanism by the BSH-PT.
finalized, it can only work well at a given narrow frequency range especially for small n , similar to the size-optimized d15 PZT wafer [23]. In order to overcome the above disadvantages of the rectangular d24 PZT wafer, a bidirectional SH0 wave piezoelectric transducer (BSH-PT) was proposed, which can be operated in a wide frequency range. As shown in Fig. 2(a) and (b), two identical rectangular face-shear (d24) PZT wafers are bonded together via their lateral faces to make up a dual-wafer transducer. The poling directions of the two PZT wafers are the same and they share a same electrode at the bonding interface. The photo of the fabricated BSH-PT is shown in Fig. 2(c). As shown in Fig. 2(d), when an electric field is applied to the BSH-PT, the face-shear deformations of the two PZT wafers are opposite due to their opposite drive field. Therefore, the induced shear stresses distributed along the PZT wafer edges are symmetric with respect to the y-axis, as shown in Fig. 2(d). Because the symmetric shear stresses distributed along the two wafers’ width direction are perpendicular to the y-axis and generated at the same time, the induced tangential displacement of particles on the y-axis must also be symmetric with respect to y-axis and thus it should be zero. In other words, SH0 waves generated by the symmetric shear stresses distributed along the transducer’s width direction will be eliminated in the y-axis direction due to the destructive interference. It should be noted that such destructive interference can always take place in the y-axis direction, so the length of the PZT wafers needs not to be multiple of the wavelength. In other words, the BSH-PT can eliminate SH0 waves in the y-axis direction over a wide frequency range. Moreover, the width of the PZT wafers also needs not to be a half wavelength of the desired SH0 wave. However, if the constructive interference condition is satisfied, enhanced single mode SH0 wave is expected to be generated in the x-axis direction.
Table 1 Material parameters of PZT wafers used in finite element simulations. Density (kg·m−3)
Relative dielectric constant
Piezoelectric constant (pC·N−1)
ρ
k11 = k22
k33
d33
d31 = d32
d15 = d24
3400
593
−274
741
s12 −4.78
s13 = s23 −8.45
s44 = s55 43.5
s66 42.6
7500 3130 Elastic compliances (pm2·N−1) s11 = s22 s33 16.5 20.7
Fig. 3. Schematics of the finite element simulation model.
directions due to the destructive interference. However, it can be seen from Fig. 1(d) that this method cannot totally eliminate the SH0 waves along the 90° and 270° directions, which can be attributed to that the rectangular d24 PZT wafer is excited by using a window-modulated toneburst of finite bandwidth, resulting in that SH0 waves whose frequencies are not at the central frequency cannot be eliminated totally. Another problem of the rectangular d24 PZT wafer is that once its size is
3. Finite element simulations Finite element simulations based on ANSYS software were 15
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Fig. 4. Finite element simulated displacement wavefields generated by the proposed BSH-PT at 180 kHz: (a) tangential displacement (SH0 wave), (b) radial displacement and (c) out-of-plane displacement in the cylindrical coordinates, (d) amplitude directivity of the excited displacement wavefields (The plots are normalized against the maximum amplitude of the tangential displacement).
Fig. 4 shows the simulated displacement wavefields generated by the proposed BSH-PT at 180 kHz. Because the particle displacement of the SH0 wave is in-plane and perpendicular to its propagating direction, the tangential displacement in the cylindrical coordinates shown in Fig. 4(a) can represent the SH0 wave. Similarly, based on the wave structures of S0 wave mode and A0 wave mode at 180 kHz·mm, the radial and out-of-plane displacements shown in Fig. 4 can be used to represent the possible Lamb waves (S0 mode and A0 mode). As expected, Fig. 4(a) shows that the excited SH0 waves are focused in the two opposite directions (0° and 180°), which can be further validated by the amplitude directivity of SH0 wave shown in Fig. 4(d). It should be noted that the length (24.8 mm) of the BSH-PT is nearly three times of the half wavelength (8.6 mm) of the SH0 wave at 180 kHz. If only a single rectangular face-shear (d24) PZT wafer with the same size is used, the SH0 wave will be amplified in the 90° and 270° directions due to the constructive interference. However, the proposed BSH-PT can totally eliminate SH0 waves in the 90° and 270° directions at 180 kHz, which demonstrates that it can generate bidirectional SH0 waves. Moreover, it can be seen from Fig. 4(b–d) that the amplitude of the tangential displacement is about one order higher than that of the radial and out-of-
performed to investigate the bidirectivity of the proposed BSH-PT. The BSH-PT in the simulation is made up of two rectangular PZT elements with the dimensions of 24.8 mm × 6.2 mm × 1 mm. The material parameters of the PZT (PZT-5H) wafers are shown in Table 1. The waveguide used in the simulation is an aluminum plate with dimensions of 400 mm × 400 mm × 1 mm and its Young’s modulus, Poisson ratio and density are 69 GPa, 0.33 and 2700 kg/m3, respectively. The BSH-PT was placed at the center of the aluminum plate and all the radiation patterns generated by the BSH-PT at different drive frequencies were extracted at a short distance (100 mm) from the center of the BSH-PT, as shown in Fig. 3. The PZT wafers were modeled by SOLID5 elements and the aluminum plate was modeled by SOLID185 elements in the ANSYS software. In order to ensure the accuracy of computational results, the largest size of elements was set to be less than 1/20 the shortest wavelength and the time step was set to be less than 1/(20fc), where fc is the central frequency of the drive signal (fivecycle Hanning window-modulated sinusoid toneburst). The amplitude of the drive signal was fixed at 20 V and its central frequency was varied from 150 kHz to 250 kHz to investigate the frequency tuning characteristics of the proposed BSH-PT. 16
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Fig. 5. Finite element simulated amplitude directivity of the displacement wavefields generated by the proposed BSH-PT at different frequencies: (a) 150 kHz, (a) 210 kHz and (c) 250 kHz (The plots are normalized against the maximum amplitude of the tangential displacement of each case).
Fig. 6. (a) Schematic of the experimental setup for investigating the bidirectivity of the proposed BSH-PT. (b) Group velocity dispersion curve of the SH0 wave and Lamb waves in a 1 mm thick aluminum plate.
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Fig. 7. (a–f) The wave signal excited by the BSH-PT at 180 kHz and measured by the d36 PMN-PT sensor along different propagation directions. (g) Radiation patterns generated by the BSH-PT at 180 kHz. The plots are normalized against the maximum amplitude of the measured SH0 wave.
setup is illustrated in Fig. 6(a). The BSH-PT used in the experiment has the same size and material parameters as that used in the finite element simulations in Section 3. The BSH-PT was bonded on a 1 mm-thick large aluminum plate using epoxy resin. A face-shear d36 PMN-PT single crystal wafer (d36 = 1600 pC/N and d31 = −360 pC/N, 5 mm × 5 mm × 1 mm) was firstly used as the sensor to check the purity of the excited SH0 wave along the direction of 0° and detect the possible wave modes in 90° direction, since it can measure both SH0 wave and Lamb waves [14]. Then both d36 PMN-PT single crystal wafers and face-shear d24 PZT wafers (6 mm × 6 mm × 1.2 mm) were used as sensors to measure the amplitude directivity of the excited SH0 wave, detailed properties of the d24 PZT wafer can be found in our previous work [25]. As shown in Fig. 6(a), the orientation of the sensor is along the red dotted line connecting the BSH-PT and the sensor, and the distance between them is fixed at 360 mm. For all the experiments, the BSH-PT was driven by a five-cycle Hanning window-modulated sinusoid toneburst signal provided by a function generator (3320A, Agilent, USA) and amplified by a power amplifier (KH7602M). The amplitude of the drive signal was fixed at 20 V, its central frequency varied from 150 kHz to 250 kHz as in this frequency range the designed PZT wafer making up the BSH-PT shows good face-shear performance. The signal of the sensors was collected by an oscilloscope (Agilent DSOX 3024A) with 128 times trace averaging. The SH0, S0 and A0 wave modes in the received signals are identified based on their different
plane displacements, which indicates that the generated A0 and S0 wave modes are negligible. To further explore the BSH-PT’s frequency dependent performances of exciting bidirectional SH0 wave, the displacement wavefields generated by the BSH-PT at 150 kHz, 210 kHz and 250 kHz were also calculated and the results are shown in Fig. 5. It can be seen that the proposed BSH-PT also exhibits perfect bidirectional properties at 150 kHz, 210 kHz and 250 kHz, which confirms that the transducer is capable of focusing SH0 wave beams in 0° and 180° directions and eliminating SH0 waves in 90° and 270° directions over a wide frequency range. Moreover, Fig. 5 shows that the ratios of the radial or out-ofplane displacements to tangential displacement for all cases are quite small, indicating that the obtained SH0 wave in each case is a perfect single mode. By comparing the radiation patterns at different frequencies in Fig. 5, it can be found that as the drive frequency turns higher, the wave energy is more concentrated along the directions of 0° and 180°. Similar phenomenon was also observed in the magnetostrictive patch transducer (MPT) [18], using which the size of MPT needed to be changed for different drive frequencies.
4. Experimental validation Experiments were then performed to investigate the proposed BSHPT’s performance on exciting bidirectional SH0 wave. The experimental 18
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Fig. 8. (a), (d), (g) Radiation patterns of the BSH-PT generated SH0 wave measured by experiments and calculated by finite element simulation at different frequencies. (b), (c), (e), (f), (h), (i) Wave signals measured by the d24 PZT wafers at different frequency in 0° and 90° directions.
element simulations shown in Fig. 4. By extracting the time interval of 120.41 μs between the drive and received signals, the group velocity of 2990 m/s can be obtained based on the distance of 360 mm between the BSH-PT and sensor, which accords well with the theoretical group velocity (3099 m/s) of SH0 wave in the aluminum plate. In order to explore whether the BSH-PT can eliminate SH0 wave in 90° direction, the wave signal along this direction was also measured by the d36 PMN-PT
group velocities and their dispersion curves in the 1 mm thick aluminum plate are illustrated in Fig. 6(b). Fig. 7(a) shows the wave signals generated by the BSH-PT at 180 kHz and measured by the d36 PMN-PT sensor placed at 0° direction. As expected, SH0 wave with high signal to noise ratio (SNR) is generated and almost no other unwanted modes (such as S0 or A0 wave mode) are observed, which are in good agreement with the finite 19
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beam divergence principle.
sensor and the result is shown in Fig. 7(f). It can be seen that no any wave modes are detected, which also accords well with the finite element simulations in Fig. 4. Fig. 7(g) shows the radiation pattern of the proposed BSH-PT at 180 kHz. The amplitudes of the measured SH0 waves at different radiation angle θ are normalized against the maximum value to compare with the simulated radiation pattern, which is also normalized. It can be seen that the experimental results are in good agreement with the finite element simulated results within the radiation angle range from −30° to 30°. The amplitude of the excited SH0 wave reaches its maximum value at 0° direction. When the deviate angle referring to the main direction (0° and 180° direction) increases, the amplitude of the SH0 wave decreases to 80% of its maxima at 15° and then further decreases to 54% of its maxima at 20°. At 30°, the amplitude of the SH0 wave is only about 17% of its maxima. Therefore, the main energy of the excited SH0 wave beam is focused within −30° to 30°. Moreover, Fig. 7(a–e) show that the excited SH0 wave beam is of high signal to noise ratio (SNR), since almost no other unwanted modes (such as S0 or A0 wave mode) are generated from 0° to 30°. When the deviate angle varies from 30° to 90°, the experimental results deviate from the simulated ones to some extent, which should be attributed to the imperfect boundary conditions in the experiments compared with that in the finite element model. Wave signals from 30° to 90° will cause the so called side lobe of SH0 wave beam. Side lobes are very common in directional transducers (for example Lamb wave transducers and bulk wave transducers) and can also appear in the response of multi-element phased arrays. Side lobes can be suppressed by improved designs, for example side lobes of the Rayleigh waves’ beam generated by EMAT can be suppressed by using the configuration of a variable-length meander-line-coil [26]. Then the BSH-PT was excited at different central frequencies to investigate its frequency tuning characteristics. By extracting amplitudes of the SH0 waves measured at different radiation directions, the radiation patterns can be obtained, as shown in Fig. 8, where the plots are also normalized against the maximum amplitude of each case. Also, the measured radiation patterns are compared with the normalized radiation patterns calculated by finite element simulation at different frequencies. It can be seen that all the experimental results are in good agreements with the finite element simulated ones. Both experiments and simulations show that the BSH-PT can focus the SH0 wave beam along 0° and 180° directions in a wide frequency range from 150 kHz to 250 kHz. Moreover, the measured wave signals show that the BSH-PT can totally eliminate SH0 wave in 90° direction and generate single mode SH0 wave in 0° and 180° directions at different frequencies, as shown in Fig. 8(b–c), (e–f) and (h–i). It should be noted that the designed width of the PZT wafers making up the BSH-PT is equal to the half wavelength of the SH0 wave at 250 kHz. However, Fig. 8 shows that the amplitude of the generated SH0 wave at 210 kHz is much larger than that at 250 kHz. Since 210 kHz is closer to the shear resonant frequency (about 190 kHz) of the PZT wafers, it indicates that the resonance is more effective to amplify the wave energy than the constructive interference. By combining Fig. 8 and Fig. 7, it can be found that the measured SH0 wave energy becomes more and more concentrated in the 0° direction, when the drive frequency varies from 150 kHz to 250 kHz. In other words, the directivity of the generated SH0 wave can be improved by increasing the drive frequency. We can qualitatively understand this phenomenon by using the beam divergence principle of bidirectional Lamb wave transducers in which similar phenomenon was also observed [10]. Wilcox et al. developed a numerical model based on Huygens’ principle to describe the wavefield generated by PVDF interdigital transducers [10]. It was found that the beam divergence angle γ is given by sin−1 (λ / l) , where λ is the wavelength and l is the finger length of the PVDF interdigital transducers. Obviously, the divergence angle γ becomes smaller when the excitation frequency increases. Since SH waves also follow Huygens’ principle, it is not difficult to infer that the proposed BSH-PT may follow the similar
5. Conclusions In summary, a variable-frequency bidirectional SH0 wave piezoelectric transducer (BSH-PT) is proposed which is made up of two rectangular face-shear (d24) PZT wafers. The performances of the proposed BSH-PT were examined by both finite element simulations and experimental testing. It is found that the BSH-PT can excite single mode SH0 wave and focus the wave energy along two opposite directions (0° and 180°) over a wide frequency range from 150 kHz to 250 kHz. The radiation patterns measured by experiments agree favorably with the finite element simulations. The good directivity of the generated SH0 wave and the frequency tunability make the proposed BSH-PT very useful for SHM of the strip like structures where one dimension is dominant over the others. Because of the focused energy within a narrow range of radiation angle and the non-dispersive characteristic of the SH0 wave, long distance is expected to be covered. Meanwhile, the proposed BSH-PT is also very useful to monitor the hollow cylindrical structures such as pipes, pressure vessels and storage tanks, since theoretically it can be used to generate circumferential shear horizontal waves propagation in the circumferential direction of a hollow cylinder [27,28]. Future works were focused on the development of analytical model to describe the wavefield generated by the proposed BSH-PT and using the BSH-PT to excite circumferential shear horizontal waves in hollow cylindrical structures. Acknowledgments H.M. acknowledges the support from the Research Foundation of Southwest Jiaotong University. F.L. acknowledges the support from the National Natural Science Foundation of China No. 11672003. References [1] J.L. Rose, Ultrasonic Guided Waves in Solid Media, Cambridge University Press, New York, 2014. [2] P.D. Wilcox, Omni-directional guided wave transducer arrays for the rapid inspection of large areas of plate structures, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (2003) 699–709. [3] D.N. Alleyne, T. Vogt, P. Cawley, The choice of torsional or longitudinal excitation in guided wave pipe inspection, Insight 51 (2009) 373–377. [4] W.A.K. Deutsch, A. Cheng, J.D. Achenbach, Self-focusing of Rayleigh waves and lamb waves with a linear phased array, Res. Nondestr. Eval. 9 (1997) 81–95. [5] L. Yu, V. Giurgiutiu, In situ 2-D piezoelectric wafer active sensors arrays for guided wave damage detection, Ultrasonics 48 (2008) 117–134. [6] M. Manka, M. Rosiek, A. Martowicz, T. Stepinski, T. Uhl, Lamb wave transducers made of piezoelectric macro-fiber composite, Struct. Control Health Monitor. 20 (2013) 1138–1158. [7] T. Stepinski, M. Manka, A. Martowicz, Interdigital Lamb wave transducers for applications in structural health monitoring, NDT & E Int. 86 (2017) 199–210. [8] X. Yan, R. Zhu, G.L. Huang, F.G. Yuan, Focusing guided waves using surface bonded elastic metamaterials, Appl. Phys. Lett. 103 (2013) 121901. [9] Z. Liu, K. Sun, G. Song, C. He, B. Wu, Damage localization in aluminum plate with compact rectangular phased piezoelectric transducer array, Mech. Syst. Sig. Process. 70–71 (2016) 625–636. [10] P.D. Wilcox, P. Cawley, M.J.S. Lowe, Acoustic fields from PVDF interdigital transducers, IEE Proc.-Sci. Measure. Technol. 145 (1998) 250–259. [11] J. Jin, S.T. Quek, Q. Wang, Analytical solution of excitation of Lamb waves in plates by inter-digital transducers, Proc. Royal Soc. A-Math. Phys. Eng. Sci. 459 (2003) 1117–1134. [12] K.I. Salas, C.E.S. Cesnik, Guided wave excitation by a CLoVER transducer for structural health monitoring: theory and experiments, Smart Mater. Struct. 18 (2009) 075005. [13] R. Ribichini, F. Cegla, P.B. Nagy, P. Cawley, Study and comparison of different EMAT configurations for SH wave inspection, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 (2011) 2571–2581. [14] H.C. Miao, S.X. Dong, F.X. Li, Excitation of fundamental shear horizontal wave by using face-shear (d36) piezoelectric ceramics, J. Appl. Phys. 119 (2016) 174101. [15] C.F. Vasile, R.B. Thompson, Excitation of horizontally polarized shear elastic-waves by electromagnetic transducers with periodic permanent-magnets, J. Appl. Phys. 50 (1979) 2583–2588. [16] H. Kwun, S.Y. Kim, Magnetostrictive sensor for generating and detecting plate guided waves, J. Pressure Vessel Technol.-Trans. ASME 127 (2005) 284–289. [17] S. Vinogradov, A. Cobb, G. Light, Review of magnetostrictive transducers (MsT)
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