A unidirectional SH wave transducer based on phase-controlled antiparallel thickness-shear (d15) piezoelectric strips

Mingtong Chen, Qiang Huan, Faxin Li,c,*

a State Key Laboratory for Turbulence and Complex Systems, and College of Engineering, Peking University, Beijing 100871, China

b Center for Applied Phyics and Technology, Peking University, Beijing 100871, China

c Beijing Key Laboratory of Magnetoelectric Materials and Devices, Peking University, Beijing 100871, China

Keywords: Guided wave Piezoelectric transducers Shear horizontal wave Thickness-shear

ABSTRACT In recent years, shear horizontal (SH) waves are being paid more and more attention to in structural health monitoring as it has only one displacement component. In this paper, a unidirectional SH wave transducer based on phase-controlled antiparallel thickness-shear (d15)piezoelectric strips (APS) is proposed. Here two pairs of identical APS were used each of which is a bidirectional SH wave transducer. By setting the interval between the two pairs of APS as 1/4 wavelength and the excitation delay between them as 1/4 period of the central operating frequency, unidirectional SH waves can be excited. Both finite element simulations and experiments were performed to validate the proposed design. Results show that SH0 waves were successfully excited only along one direction and those along the unwanted directions were suppressed very well. The proposed unidirectional SH wave transducer is very helpful to study the fundamentals and applications of SH waves.

In the structural health monitoring (SHM) and nondestructive testing (NDT) field, ultrasonic guided waves are of great importance because of its less dissipation and thus long-distance coverage. Compared with the Lamb waves, shear horizontal(SH) waves only have one displacement component and the fundamental mode (SH0) is totally non-dispersive, which can effectively reduce the complexity of signal processing and defect locating. However, it is difficult to excite pure SH waves effectively,thus SH waves were less used than Lamb waves in engineering.Traditionally, SH waves were usually generated by the electromagnetic acoustic transducer (EMAT) which is bulky and of very low efficiency in energy conversion [1].

Early in 1979, a type of noncontact electromagnetic transducer with the configuration of axially wound coil combined with a periodic permanent magnet (PPM) had been proposed by Vasile and Thompson [1] to excite SH waves in non-ferromagnetic metallic plates. The PPM EMAT is a bidirectional SH wave transducer. Based on phase-controlled excitation, unidirectional SH waves can also be excited using PPM EMATs [2]. For ferromagnetic materials, a magnetostrictive sensor consisting of a channel-shaped core and coils wound was capable of generating and detecting both Lamb and SH waves [3]. Lee et al. [4-6]had investigated the radiation patterns of Lamb and SH waves generated by a circular magnetostrictive patch transducer and proposed a new specially-configured planar solenoid array to focus SH wave beams. Liu et al. [7] also developed a direction-tunable shear-horizontal mode array magnetostrictive patch transducer based on the magnetostrictive effect to excite SH0waves,and the acoustic field distribution depends on the fan-shaped meander coils and permanent magnets. Bidirectional and unidirectional SH waves have been excited by various EMATs [8].Recently, Sun et al. [9, 10] proposed a newly designed electromagnetic acoustic transducer for unidirectional focusing of SH waves to inspect plates. However, the heavy testing equipment is only suitable for non-destructive testing rather than structural healthy monitoring. Moreover, high power supply must be used to generate SH waves, otherwise the defect signal might be masked by noise signals. Based on the EMATs, Ogi et al. [11-13]explored mode conversion of SH guided wave when it impinges on smooth defects in plates and developed a useful technique to detect corrosion defects on the outer surfaces of steel pipelines,even if the protective resin coating is tightly glued on the pipes.Petcher and Dixon [14] and Kubrusly et al. [15] discussed the interference patterns created as the multiple SH mode mixing, and the problem caused by the interference patterns which would occur on industry. Some researches on fundamental characteristics of SH waves and defect inspection based on SH waves had also been conducted based on EMATs [16-18].

Compared with EMATs, piezoelectric transducers are much more effective in energy conversion and easier to manipulate.Miao et al. [19, 20] proposed a new face-shear (d24) piezoelectric transducer which can excite and receive single-mode SH0waves.What's more, a variable-frequency bidirectional SH wave transducer consisted of two rectangular face-shear piezoelectric transducer was also developed. Through geometrical parameter optimization of ad15piezoelectric strip, Lamb waves had been suppressed and plane SH0wave can be excited in a narrow frequency range [21]. Meanwhile, Omni-directional SH wave transducers were also developed, based on the synthetic circumferential polarized ring usingd15andd24elements [22, 23], or more effectively based on thick-poled, thickness-shear (newd15) piezoelectric rings [24, 25]. The feasibility of structural health monitoring using SH wave transducers were also validated based on sparse array and phased array [26, 27]. Recently, Chen et al. [28]proposed a tunable bidirectional SH wave transducer based on antiparallel thickness-shear (d15) piezoelectric strips (APS),which well suppressed the Lamb waves and focused the SH wave energy in two opposite directions. Furthermore, the APS based bidirectional transducer can suppress SH0wave and excite single-mode SH1wave, which is very useful to study the fundamentals and applications of SH waves.

As shown in Fig. 1a, a pair of antiparallel alternating shearing line forces with the interval of half-wavelength (λ/2), can excite bidirectional SH waves along both the positive and negative directions ofx1[28]. Meanwhile, the excited Lamb waves along thex2direction will diminish via destructive interference. To excite unidirectional SH wave, two identical pairs of anti-parallel shearing forces are required and the phase-controlled excitation technique should be employed. As shown in Fig. 1b, the distance between the centers of two pairs antiparallel shearing forces is 1/4 wavelength (λ/4) and the excitation phase difference between them is π/2. The excited SH wave will be strengthened along thex1positive direction via constructive interference and will diminish along thex1negative direction via destructive interference. In this work, thickness-shear (d15)piezoelectric strips driven by electric field are used to simulate the shearing line forces, and the phase difference is controlled by driving signals. Compared with the PPM EMAT, the phasecontrolled two pairs of antiparalleld15piezoelectric strips (PCAPS) is expected to excite strong enough unidirectional SH waves because of the high energy conversion efficiency of the contact mode piezoelectric transducers.

Three-dimensional finite element simulations based on ANSYS software were performed to investigate the directivity of the proposed unidirectional piezoelectric SH wave transducer. The transducers in the simulation is made up of four PZT-5H strips with the dimensions of 20 mm×2 mm×1 mm. The materials parameters of PZT-5H are shown in Table 1. The waveguide used in the simulation is an aluminum plate with the dimensions of 400 mm×400 mm×2 mm and its density, Young's modulus, Poisson ratio are 2700 kg/m3, 71 GPa and 0.33, respectively.The transducer was placed at the center of the aluminum plate.SOLID 5 and SOLID 185 elements were respectively used to simulate the piezoelectric strips and aluminum plate in the ANSYS software, as shown in Fig. 2a. In order for identification of wave modes, Fig. 2b presented the group velocity of guided waves for 2 mm-thick aluminum plate under different frequency. SOLID 5 is 3-D coupled-field solid and SOLID 185 is 3-D eight-node structural solid. In order to ensure the accuracy of computational results, the largest element size was 1/15 of the exciting wavelength and the time step size was 1/20 of the central period of the driving signal. The amplitude of the driving voltage signal was fixed at 20 V. Meanwhile, two five-cycle Hanning windows-modulated sinusoid tone burst with the phase difference of π/2 were applied to the two pairs of APS transducer simultaneously.The radial displacement component, tangential displacement component, and out-of-plane displacements componentwere collected at the distance (100 mm) from the geometric center of the plate.

Fig. 1. Guided waves in a large plate generated by a antiparallel shearing line forces and b two pairs of phase controlled antiparallel shearing line forces.

Table 1 Material properties of the PZT-5H piezoelectric ceramics in the simulations

Fig. 2. a Schematics of the finite element simulation model. b Group velocity verse frequency for SH0 wave and Lamb waves in a 2 mm-thick aluminum plate.

Fig. 3. Experimental setup for testing the performances of the proposed unidirectional SH wave transducer.

Experiments were then performed to validate the proposed PC-APS transducer's performance on exciting unidirectional SH0waves and the experimental setup is illustrated in Fig. 3. The PCAPS transducers used in the experiment have the same size and material parameters as that in the former finite element simulations. In the directivity testing, a thin plate with dimensions of 1000 mm×1000 mm×2 mm was used as the waveguide and the PC-APS transducer was bonded on the center of the plate using 502 epoxy adhesive. In order to explore the unidirectional of proposed transducers, all excited wave signals in different directions should be detected. Along the excited SH0wave direction,the measured amplitude had varied with angle largely and therefore the receivers were placed tightly with 5° interval. The angle interval was set to 10° perpendicular to excited SH0wave direction as the measured amplitude could be almost ignored. Both thed15type sensors with the dimensions of 12 mm×2 mm×1 mm and thed31type circle sensors with the dimensions of 6 mm×6 mm×1 mm were used as receivers. Thed15type sensors for receiving SH waves and thed31type sensors for receiving Lamb waves were bonded at the distance of 360 mm from excitation source and 260 mm along the 0° direction, respectively, as shown in Fig. 3. Both pairs of APS transducers were driven by five-cycle Hanning windows-modulated sinusoid tone burst voltages of 50 V with the phase difference of π/2, which was provided by a dual-channel function generator (33520A, Agilent,USA) and amplified by two identical power amplifiers(KH7602M, KROHN-HITE, USA). An oscilloscope (DSO-X 3024T, Agilent, USA) with 256 times trace averaging was used to collect and record all the received signals.

A series of finite element simulations were performed to validate the performance of the proposed unidirectional SH wave transducer based on PC-APS. First, the guided waves excited by two pairs of anti-parallel shearing line forces with the same phase and with a phase difference of π/2 were comparatively simulated to examine the validity of the proposed design. Then,the effects of the line force interval (which determines the driving frequency) on the radiation angles of the excited SH wave were investigated. Finally, thed15PZT strips' performances on excitation SH wave were examined and compared with that of the shearing line forces.

Fig. 4. Finite element simulated results on displacements of different guided wave modes generated in a 2 mm-thick aluminum plate by using antiparallel shearing line force (SLF) of 20 mm length. Left: two pairs of same phase SLF with different intervals (driving frequencies). a 8 mm,98 kHz and c 4 mm, 196 kHz; Right: two pairs of SLF with the phase difference of π/2 and with different intervals. b 8 mm, 98 kHz and d 4 mm,196 kHz.

Figure 4 shows the simulated various displacements of different guided wave modes generated at 98 kHz (with the strip interval of 8 mm) and 196 kHz (with the strip interval of 4 mm) in a 2 mm-thick aluminum plate by using 20 mm long shearing line force and all nodes of the 20 mm long line were prescribed with in-plane pressure load (20 N). The amplitude of S0wave, SH0wave, A0wave were denoted by the radial displacement, the circumferential displacement, the out-of-plane displacement, respectively. It can be seen from Fig. 4 that when the two pairs of shearing line forces have the same phase, SH0wave can be excited with the maximum amplitudes along 90° and 270° directions. The ratio of maximum amplitudes of S0and A0to maximum amplitudes of SH0(abbreviated as LSR) are both less than 10% at 98 kHz, indicating that the excited Lamb waves can almost be ignored, as shown in Fig. 4a. Furthermore, the radiation angle of the excited SH0wave decreased considerably when the strips interval reduced to 4 mm, corresponding to the driving frequencies of 196 kHz, and the LSR was further reduced to below 5%, as shown in Fig. 4c. When the two pairs of shearing line force have π/2 phase differences, the SH0wave along the 270°direction has disappeared and only SH0wave were excited, as seen in Fig. 4(b, d). Meanwhile, the Lamb wave were also suppressed well. Note that there appeared small grating lobes of SH0wave along 230° and 310° with the amplitude about 10% of the main lobe at 98 kHz and less than 5% at 196 kHz, seen in Fig. 4(b,d). From above, it can be concluded that unidirectional SH0waves were successfully excited by the phase-controlled antiparallel shearing line forces.

The finite element simulations ond15piezoelectric strips with the same length of the line forces, i.e., 20 mm, width of 2 mm, and thickness of 1 mm were further conducted, and the results were shown in Fig. 5. It can be seen that the wave pattern generated byd15piezoelectric strips in Fig. 5 is similar to that generated by shearing line forces in Fig. 4. The excited LSR for thed15piezoelectric strips case is also close to that for the shearing line force case, indicating that the effect of strips width and thickness is almost negligible. When the two pairs of antiparalleld15APS were driven by the same phase voltage, bidirectional SH0waves were excited along 90° and 270° directions. Also, the radiation angle of SH0waves decreased with the increasing driving frequency, as shown in Fig. 5(a, c). As we expect, only unidirectional SH0waves were excited when the applied voltage has a π/2 phase difference. Note that the Lamb waves cannot be suppressed as well as in the shearing line force case, but the LSR is still below 10% which is also quite good. Here increasing the driving frequency has little effect on suppressing the Lamb waves but is still effective on focusing the SH wave energy, which is also slightly different from the shearing line forces case.

Fig. 5. Finite element simulated results on displacement of different guided wave modes generated in a 2 mm-thick aluminum plate by using d15 piezoelectric strips with the thickness of 0.8 mm and width of 2 mm. Left: two pairs of antiparallel d15 APS driving under the same phase voltage for different intervals. a 8 mm, 98 kHz and c 4 mm, 196 kHz; Right: two pairs of APS driving with the phase different of π/2 for different intervals. b 8 mm, 98 kHz and d 4 mm, 196 kHz.

Experiments were then conducted to examine the performances of the designed unidirectional SH wave transducer. Since the generated wave patterns were symmetric about the 90° direction, the signals from 0° to 90° directions were collected and the responses from other directions were obtained by mirroring and switching the phase difference from π/2 to be -π/2.

Figure 6 shows that the wave signals generated by the PCAPS unidirectional transducer at 98 kHz were measured by thed15PZT strip sensors along different propagation directions and thed31PZT disk sensor along 0° and 180° directions respectively.The wave type was identified by travelling speed through continuous wavelet transform technique. As expected, unidirectional SH0waves with high signals to noise ratio had been generated.From Fig. 6(a-f), it can be seen that the amplitude of the excited SH0waves reaches its maxima at 90° direction and gets minima at the 270° direction. The ratio of the minimum amplitude to maximum amplitude is only about 5%, indicating that almost no SH0wave was excited along the 270° direction.

Figure 7 presents the wave patterns generated by the two pairs of APS transducers driven under the same phase and the phase difference of π/2 respectively. Overall, the experimental results are consistent with the FEM simulation results in Fig. 5,i.e, the SH0waves along the 270° direction had been well suppressed. Also, the radiation angle decreased with the increasing driving frequency. However, the measured wave pattern is discontinuous because of the discrete SH wave receivers. As shown in Fig. 7b, at 98 kHz, the maximum amplitude of the excited SH0wave in the unwanted directions (around 270°) is less than 15%of the maximum amplitude along 90° direction. Considering the wave profile in Fig. 7b, the radiated wave energy in the unwanted directions is estimated to be less than 2% of the total wave energy. When the driving frequency was increased to 196 kHz, the ratio of the excited SH0amplitude in the unwanted direction to the maximum amplitude increased to be about 20%which is along 240° and 300° directions, as seen in Fig. 7d. Accordingly, at 196 kHz, the radiated wave energy in the unwanted directions increased to be about 4% of the total wave energy,which is still very desirable.

It should be noted that here the driving frequency cannot be increased above 196 kHz because the strip interval cannot be decreased to be less than 2 mm due to the employed 2 mm-wided15PZT strips. Actually, this limitation can be improved by reducing the width of the employedd15strips and/or changing the interval between the two pairs of APS fromλ/4 to be (n+1/4)λand setting the driving phase difference to be 2nπ+π/2 (wherenis an integer).

Fig. 6. Wave signal excited by the PC-APS at 98 kHz measured by the d15 PZT strips a-f along different directions and the d31 PZT disk along g 0°and h 180° directions.

Fig. 7. Wave patterns excited by the 20 mm-long APS. Left: APS driving with the same phase for different intervals. a 8 mm, 98 kHz and c 4 mm,196 kHz; Right: APS driving with the phase difference of π/2 for different intervals. b 8 mm, 98 kHz and d 4 mm, 196 kHz.

The above simulation and experiment results had shown that the proposed PC-APS transducer can effectively excite unidirectional SH waves. As the unidirectional SH wave transducer is developed based on our previously proposed bidirectional SH wave transducer using APS [28], some characteristics of the APS bidirectional transducer are also applicable to the PC-APS unidirectional transducer, e.g., the working frequency of this transducer can be tuned by varying the strip interval, the radiation angle of the excited unidirectional SH wave can be fairly reduced by extending the strip length, increasing excitation frequency and superposition of multiple strips.

In summary, we proposed a unidirectional SH wave transducer based on phase-controlled antiparalleld15PC-APS. FEM simulations and experimental testing were both conducted to evaluate the proposed transducer's performance. Results show that unidirectional SH0waves were successfully excited and the radiation angle of the excited SH wave can be effectively reduced by increasing the driving frequency (decreasing the strip interval). The proposed PC-APS based unidirectional SH wave transducer can be widely used in studying the fundamentals and applications of SH waves, such as scattering, refraction, mode conversion, and structural health monitoring, etc.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant 11521202).