Shear Horizontal Research Articles

Crack-Depth Estimation in Concrete Elements Using Ultrasonic Shear-Horizontal Waves

Determination of the depth of surface-opening (visible) cracks is of critical importance for evaluating the structural safety of concrete elements. Accurately determining the crack depth with traditional nondestructive testing methods, however, is challenging. This study developed a new method using ultrasonic shear-horizontal (SH) waves to detect the depth of surface-opening cracks in concrete. The method is based on the diffraction of ultrasonic SH waves at the bottom edge of a crack. An off-the-shelf ultrasonic imaging device was used with dry-point contact transducers having a set of transmitters and a set of receivers performing in a pitch-catch configuration. SH waves are superior to other waves in data interpretation because the SH waves have a higher signal-to-noise ratio as the only wave type generated by their transmitter and without mode conversion after diffraction. Thus, accurately identifying the travel time of diffracted SH waves in the time domain is very achievable. The crack depth can be calculated with the two-way travel time of SH waves, the spacing between the transducers, and the SH-wave speed. The method was validated with a-finite element model and experimental data from two case studies. Results indicated that this method can significantly improve the accuracy of determinations of the depth of surface-open cracks compared with the ultrasonic longitudinal wave method.

A Novel Surface Acoustic Wave Biosensor for Real-Time Monitoring of Cell Contractile Properties

Introduction Contraction of cardiomyocytes is a vital property of the heart and its assessment is significant for drug discovery. At present, many researches focus on the electrophysiology detection through microelectrode arrays (MEAs) [1-2]. However, mechanical properties of cardiomyocytes is also critical for many biological processes including cell growth, motility, division, differentiation, and tissue homeostasis [3]. Currently, the atomic force microscope (AFM) has been used to measure the contractile properties of cardiomyocytes. However, the AFM is only suitable for single cells and can only measure one cell at one time. Therefore, it’s necessary to develop a detection system that can monitor the contractile properties of cardiomyocyte in a real-time and dynamic way.Recently, the surface acoustic wave (SAW) sensor has been greatly developed as a well-performed mass sensing device for label-free immunoassay due to its attractive advantages, including real-time monitoring and simplicity of use [4]. In particular, the guided shear horizontal (SH) SAW sensor, which is also known as the Love Wave sensor, has shown its advantages in biosensor applications due to its high sensitivity and stability in the liquid phase [5]. Hence, SAW is a device capable of monitoring viscoelastic properties of a population of cells, which correlates with stiffness, in a non-invasive, label free and continuous manner up to several days to weeks.In this study, a Love Wave sensor was used to study the contractile properties of HL-1 cardiomyocytes, where changes in insertion loss and phase position of the sensor can reflect the mechanical changes (contraction and viscoelasticity). Different compounds were added to test the different effects on the contractile properties of HL-1 cardiomyocytes, and the signals were analyzed by principal component analysis (PCA). Method In this study, the Love Wave sensor is constructed based on a piezoelectric quartz substrate. Interdigitated transducers (IDTs) with Ti/Au (20/200 nm) are deposited to generate pure shear horizontal acoustic waves. The input and output IDTs electrodes consist of 50 split-finger pairs with a wavelength λ=28 μm, which determines the center frequency of the sensor to be about 160 MHz [4]. The distance between IDTs centers is 200λ and the acoustic aperture is 75λ. Afterwards, the IDTs patterned substrate is guided with a 3 μm SiO2 film deposited by plasma enhanced chemical vapor deposition (PECVD). Au layer (200 nm) is deposited on top of guiding layer to improve the cell attachment on the sensor surface.A polydimethylsiloxane (PDMS) chip was designed and used as the cell culturing chamber. The height and volume of this cavity are about 10 mm and 150 μL, respectively. A portable and miniaturized multi-channel Love Wave sensor detection system was developed to detect both the insertion loss and phase signals of sensors. And then, HL-1 cardiomyocytes with 10,000 cells were seeded on the sensor chip. To test the function of the detection system, isoprenaline (ISO) and verapamil (VRP) with different concentrations were used to induce changes in the contractile properties of HL-1 cells. Results and Conclusions VRP is a calcium channel antagonist that blocks the L-type calcium channel and prevents calcium influx into the cell, thereby decreasing the cardiomyocyte contraction force. With the addition of VRP solutions, the insertion loss of Love Wave sensors increased, and the magnitudes of insertion loss increased with the increase of VRP concentration. Our results indicated that the stiffness of living HL-1 cells decreased after VRP administration. Moreover, the higher the VRP concentration is, the softer the HL-1 cells are within the dosage range tested. In contrast to VRP, ISO is positive inotropic drug. After ISO treatment, HL-1 cells wrinkled due to the traction forces. Therefore, the higher the ISO concentration, the larger the traction force and the tighter is the contact of the cells with the sensor substrate, and the stiffer the cells. Moreover, the responses of SAW sensor treated by VRP and ISO could be distinguished by PCA.As far as we know, this is the first report that study the contractile properties of a cardiomyocytes cell line based on a SAW biosensor. The affection on cardiac contractility of different compounds can be monitored by recording the changes in insertion loss and phase position of the SAW sensor. Our results demonstrated that the SAW sensor is a potential new tool for in vitro cardiac contractility evaluation and has promising applications in drug discovery, safety screening and many other fields.

Giant Magnetoelastic Coupling in a Love Acoustic Waveguide Based on TbCo2 / Fe Co Nanostructured Film on ST-Cut Quartz

Coupling between dynamic strain and magnetization in ferromagnetic thin films has attracted special consideration as it presents both intriguing fundamental physics problems and technological importance for potential multi-functional devices and information handling. The dynamic strain can be generated by acoustic waves including bulk, surface or guided waves. In this work, we propose the theoretical and experimental investigation of the interaction of pure shear horizontal (SH) wave with a uniaxial multilayered TbCo2/FeCo thin film in a delay line configuration fabricated on Quartz ST-90X cut. We evaluate theoretically the evolution of phase velocity as a function of magnetic field and experimentally the variation of the transmission coefficient. A piezomagnetic model was developed allowing us to calculate the elastic stiffness constants of the multilayer as a function of the applied magnetic field. The model was also implemented for acoustic waves dispersion curves calculation. We show that the evolution of phase velocity is dominated by the C66 elastic stiffness constant variation as expected for the case of shear horizontal surface wave. The fabricated device let us exciting both fundamental and third harmonic shear mode at 410 MHz and 1.2 GHz, respectively. For both modes, the theoretical results corroborate very well the experimental ones. At 1.2 GHz the mode exhibits a maximum phase velocity shift close to 2.5% and an attenuation reaching 500 dB/cm, for a sensitivity as high as 250 ppm/Oe. The reported theoretical model and experimental results are of tremendous interest for the development of advanced devices for magnetic field sensing applications as well as investigating magnon-phonon interaction at a fundamental level.

Single SH guided wave mode generation method for PPM EMATs**Project supported by the National Natural Science Foundation of China (Grant No. 51977044).

Using periodic permanent magnet (PPM) electromagnetic acoustic transducers (EMATs), different shear horizontal (SH) guided wave modes can form simultaneously in some situations, which can interfere with the inspection. The main cause of this phenomenon (typically named multiple modes) is related to the frequency bandwidth of excitation signals and the transducer spatial bandwidth. Simply narrowing the frequency bandwidth cannot effectively limit the number of different SH modes. Previous researches showed that unnecessary SH wave modes can be eliminated by using dual EMATs. However, in practical applications, it is more convenient to change the excitation frequency than to use dual EMATs. In this paper, the stress boundary conditions of the PPM-EMAT are analyzed, the analytical expression of SH guided wave is established, and the magnitude of SH guided wave mode under continuous tone and tone-burst input is obtained. A method to generate a single SH mode by re-selecting an operating point is proposed. Furthermore, the influence of the frequency bandwidth of the tone-burst signal is analyzed. Finally, a single SH mode excitation is achieved with tone-burst input.

Oblique Point-Focusing Shear-Horizontal Guided-Wave Electromagnetic Acoustic Transducer With Variable PPM Spacing.

We realized a phase-coherent oblique point-focusing shear-horizontal (SH) guided-wave electro- magnetic acoustic transducer (EMAT) composed of variable-spacing periodic permanent magnets (PPMs) and racetrack coils. For traditional focusing transducers, the necessary focal position adjustment in defect detection requires a redesign of the coil structure. More conveniently, this new transducer structure arrangement can achieve wave focusing and focal position change by rationally adjusting the layout of the PPM without changing the coil structure. Simulation results show that this newly designed transducer has good focusing performance: it can successfully focus the signal to a preset point, and the signal amplitude is nearly double that of the nonfocusing side. In addition, the focusing performance optimization of the transducer has been studied. The experimental results agree well with the actual location and size of a defect, which verifies the effectiveness of the newly designed focusing transducer in defect detection.

Determining Anti-plane responses of a semi-circular alluvial valley embedded in a single layered half-space

This paper proposes a modified hybrid computational method, comprising finite element method and a Lamb series for a single layered half-space, to derive displacement amplitude (|uyjAV|) in a field that includes a semi-circular alluvial valley (SCAV) embedded within a single layered half-space subjected to shear horizontal (SH) waves. Variations in |uyjAV| associated with depth (from the free surface through the SCAV and layered medium to the half-space) and site effects were also examined under various incident angles (θ2) and dimensionless frequencies (ζ). Our analytical solutions, based on a theoretical model of the single layered half-space, revealed the thickness effects and the resonance frequencies (RFs) under various θ2, due to a soft layered medium. We compared the resulting |uyjAV| value with those of an SCAV embedded in a half-space (i.e., |uyjav|) and theoretical solutions based on a single layered half-space (i.e., |uyjf|) under RFs with various θ2. We discovered that due to the embedding of an SCAV in the single layered half-space, the thickness effects created by that space were a major contributor to site effects. The response amplitudes at the free surface were also magnified by the enlargement effect of the SCAV. Additional numerical simulations were conducted to obtain responses of |uyjAV| under ζ ranging from 0.01 to 2.0. These results support our discovery that thickness effects dominate the site effects. This paper provides a valuable reference to further our understanding of site effects associated with surface irregularities in the single layered half-space.

In situ steering of shear horizontal waves in a plate by a tunable electromechanical resonant elastic metasurface

A multifunctional electromechanical coupling metasurface is proposed to steer elastic shear horizontal (SH) waves. The horizontal shear deformation of the metasurface is coupled with a shunting circuit by in-plane polarized piezoelectric patches. A prospective phase distribution along the metasurface can be achieved by adjusting the negative capacitances of the shunting circuit to change the electromechanical resonant response. Multiple functions are demonstrated, including wave focusing and anomalous refraction of plane waves in different frequencies. In addition, an asymmetric wave transmission is produced by designing a dual-layer metasurface. Results show that this metasurface opens up a way toward advanced electromechanical coupling and tunable manipulation of elastic SH waves.

A New General Form of 2-D Coupling-of-Modes Equations for Analysis of Waveguiding in Surface Acoustic Wave Devices.

Since surface acoustic waves (SAWs) are composed of multiple displacement components, their slowness curves sometimes exhibit a more complex shape rather than elliptical or hyperbolic. As a result, the parabolic approximation of 2-D coupling-of-modes (2-D COM) equations is invalid for analysis of waveguiding in such SAW devices. Thence, this paper develops a new general form of 2-D COM equations based on the basic 2-D wave equations of SAWs which contain two displacement components. The fundamentals of the equations were established and the procedures for determining 2-D COM parameters were presented in detail. The new equations were embedded in the partial differential equation (PDE) mode of COMSOL for the simulation of different types of SAWs, including Rayleigh and shear-horizontal (SH) SAWs on ST-quartz and 42°YX-LiTaO3 (42-LT) substrates, respectively. By comparing the calculated results with 1-D COM, parabolic 2-D COM, extended thin plate model, 3-D finite-element method (FEM) calculated results, and the measured result, the applicability of these equations was verified.

Analysis of mechanical vibration (SH wave) in Piezo-composite plates

The present problem aims to study the propagation behaviour of Shear Horizontal (SH) surface waves in a composite structure comprising of functionally graded piezoelectric plate fused with a porous piezoelectric plate. The material properties of the functionally graded piezoelectric material (FGPM) are assumed to be vary in quadratic manner. Method of separation of variables is used to obtain the solutions for the displacement and stress components in both the media. Solutions are obtained in terms of modified Bessel functions of first and second kinds. Dispersion relations are obtained for both the electrically open and short cases. Effects of thickness of the plates, gradient parameter, dielectric coefficient and piezoelectric coefficient on dispersion curve have been marked distinctly and portrayed through graphs. The electromechanical coupling factor is also plotted against wave number. Findings of the present investigation may set guidelines for the designing of more efficient Surface acoustic wave (SAW) devices.

Formation mechanism of SH guided wave in weld seam

Shear horizontal (SH)-guided wave detection of weld seams is a new type of weld detection technology. To better apply SH-guided waves to weld detection, it is necessary to study the formation mechanism of SH-guided waves and to identify weld structures suitable for SH-guided wave detection. Here, we used the theory of peridynamics as well as the reflection and refraction of SH-guided waves in different media. Theoretical analysis suggested that the formation of an SH-guided wave is related to the incident angle of the guided wave, and the formation of SH-guided waves is related to the weld height and the weld interface. The influence of different weld heights and weld interfaces on the formation of SH-guided waves was studied by numerical simulation. We concluded that the weld height is beneficial to the formation of the guided wave because the strength of guided wave in weld seam and steel plate can reflect the refraction and reflection characteristics of the SH wave. More energy is trapped in the weld with increasing weld height, and the radiation rate of SH-guided waves linearly decreases. Higher welds will disperse the SH-guided waves and confuse the signals. This makes the echo subtle and is not conducive to the detection of weld defects. Therefore, we concluded that weld heights over 5% of the weld width are more conducive to detection of weld defects. After analysis of the weld interface, we concluded that the radiation rate of SH-guided waves in a U-type interface and V-type interface are much higher than those a type II interface: These are not conducive to the formation of weld-guided waves and lead to low sensitivity for SH-guided wave detection.

Surface wave transference in a piezoelectric cylinder coated with reinforced material

The present study deals with the propagation of a polarized shear horizontal (SH) wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder. The interface of the two media is assumed mechanically imperfect. For obtaining the dispersion relation, the mathematical formulation has been developed and solved by an analytical treatment. The effects of various parameters, i.e., the thickness ratio, the imperfect interface, the initial stress, the reinforcement, and the piezoelectric and dielectric constants, on the dispersion curve are observed prominently. The dispersion curves for different modes have been also plotted. The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.

Interfacial imperfection study in pres-stressed rotating multiferroic cylindrical tube with wave vibration analytical approach

In the present paper, two distinct multiferroic composites are taken into account, i.e., PE (piezoelectric)/PM (piezomagnetic). An analytical technique is applied to study the shear horizontal (SH) wave propagation in a layered pre-stressed rotating cylindrical tube structure consisting of a PE material layer which is wrapped on PM material having an imperfect interface. It is assumed that consider interface is mechanical, electrically and magnetically damaged. Dispersion relations are obtained for electrical-magnetic open/short boundary conditions. Distinct graphs are drawn (numerically) to exhibit the influence of parameters like rotation, initial stress and imperfect parameters (mechanical, electrical and magnetic) on phase velocity. Parametric results on the phase velocities yield a significant conclusion of which some are: (a) Performance has Piezo-composites have a great impact on phase velocity. (b) The mechanical imperfection affects the more on phase velocity along with the combination of thickness ratio and wave number in respect to electrical -magneto imperfection (c) The PE/PM stiffening can monotonically increase the speed of phase.

On the propagation of nonlinear SH waves in a two-layered compressible elastic medium

We examine nonlinear shear horizontal (SH) waves in a two-layered medium of uniform thickness. Materials in both layers having different material properties are assumed to be nonlinear elastic, homogeneous, compressible and isotropic. Furthermore, $$c_1<c_2$$ is chosen where $$c_1$$ and $$c_2$$ are the linear shear wave velocities of the top and bottom layers, respectively. The propagation of SH waves in a two-layered medium exists only if either of the inequalities $$c_1<c< c_2$$ and $$c_1<c_2< c$$ is satisfied where c refers to the phase velocity of waves. The dispersion relations of linear SH waves corresponding to these phase inequalities are obtained. Then, the self-modulation of nonlinear SH waves is investigated by using an asymptotic perturbation method for each case. By balancing dispersion and weak nonlinearity, it is shown that the self-modulation of the first-order slowly varying amplitude of nonlinear SH waves is characterized asymptotically by nonlinear Shrodinger (NLS) equation. The form of NLS equations corresponding to each phase inequality is identical except their coefficients. Then, the effects of nonlinearity of the materials in layers on the linear stability of the solution of NLS equation and on the existence of solitary wave solutions are studied by employing several fictive material parameter models.

Mixed third harmonic shear horizontal wave generation: interaction between primary shear horizontal wave and second harmonic Lamb wave

The third harmonic shear horizontal (SH) waves in a weakly nonlinear plate provide new possibilities for incipient damage detections. The understanding of their generation mechanism, however, is limited to the intuitive process of cubic self-interaction of the primary SH waves. By considering both the third order and fourth order elastic constants, this paper reports the discovery of a new generation mechanism, referred to as mixed generation, which results from the mutual interaction between the primary SH waves and their induced second harmonic Lamb waves. Compared with linearly cumulative third harmonic SH waves induced by the cubic self-interaction of the primary SH waves, the mixed third harmonic SH wave amplitude also increases with the wave propagating distance but in a wavering manner according to the phase velocity matching condition. Upon establishing a complex-domain superposition method which allows a precise extraction of the third harmonic responses, the significance and the propagating characteristics of the mixed third harmonic SH waves are numerically investigated through finite element simulations. Experiments are then conducted with a dedicated subtraction scheme to highlight the material nonlinearity of interest. A gel test is designed and carried out to identify the two types of third harmonic SH wave components from the measured time-domain signals. Both numerical and experimental results confirm the existence and the significance of the mixed third harmonic SH generation mechanism, which may impact on further applications, especially underwater damage inspections.

Point-Focusing of Shear-Horizontal Wave Using Fan-Shaped Periodic Permanent Magnet Focusing Coils EMAT for Plate Inspection

Ultrasonic guided wave testing method is very effective in safety monitoring of complex structures, such as large-scale tank floor and industrial metal plate. The fundamental shear horizontal (SH) wave mode with the Lorentz force mechanism has the advantage that the propagation velocity does not change with the frequency. However, it is hard to recognize the dispersed ultrasonic signal accurately due to the bidirectional propagation characteristics of the SH guided wave. Therefore, a new transducer structure with a fan-shaped periodic permanent magnet (PPM) and centripetal conductor has been designed to achieve guided wave focusing and signal enhancement. Compared with the traditional transducers, the new-designed transducer has been proved to be more effective in energy focusing on the simulation and experimental verification. For the new structure of the transducer, the aperture angle, focusing radius, and coil rotation angle are studied in detail in this paper. The results show that, as the aperture angle and the coil rotation angle decrease, the signal intensity becomes higher at the focusing position. Moreover, as the focal radius increases, the amplitude of the ultrasonic signals on the focusing side and the divergent side will decrease, while the difference between the two sides will increase exponentially. In the defect detection in this paper, the reflected signal intensity of the new-designed fan-shaped PPM focusing coils electromagnetic acoustic transducer (EMAT) is approximately two times that of the traditional parallel PPM parallel coils EMAT. Therefore, the newly designed EMAT is of great significance for the signal enhancement.

A tunable bidirectional SH wave transducer based on antiparallel thickness-shear (d15) piezoelectric strips

Guided wave based defects inspection is very promising in the field of structural health monitoring (SHM) and nondestructive testing (NDT) due to its less dissipation and thus long distance coverage. In comparison with the widely used Lamb waves, shear horizontal (SH) waves are relatively simple but less investigated probably due to the traditional notion that SH waves were usually excited by electromagnetic acoustic transducers (EMAT). In this work, we proposed a tunable method to excite single-mode bidirectional SH waves in plates using antiparallel thickness-shear (d15) piezoelectric strips (APS). The proposed SH wave driving mechanism here is similar to that by using the periodic permanent magnetics (PPM) based EMAT with the period of strips equal to half of the wavelength. Both finite element simulations and experiments were conducted to validate this transducer in excitation of bidirectional SH waves. Results show that the Lamb waves excited by single piezoelectric strip can be suppressed very well. The radiation angle of the excited bidirectional SH wave can be reduced by extending the strip length, increasing the driving frequency or using more strips. Moreover, the APS transducer can selectively excite SH1 wave and suppress the SH0 wave at 174 kHz and 273 kHz in a 10 mm-thick aluminum plate. Considering its simple structure, flexible design and low excitation energy, the APS SH wave transducer is expected to be widely used in near future.

Thermal Effect on Band Gaps of 1D Metallic Phononic Crystals

We have investigated thermal effect on band gaps of shear horizontal (SH) waves propagating through a layered metallic periodic structure. For a metallic material, the lattice length varies slightly with temperature while the Young’s modulus is strongly thermosensitive. Firstly, the dispersive equation without thermal effect was derived by the transfer matrix method. Secondly, the thermal effect on the material coefficients was investigated. Finally, the dispersive curves at different temperatures with changing incident angles were drawn. It reveals that the band gaps get a greater impact in high-frequency regions than those in low-frequency regions. The results can provide theoretical basis for the production of phononic crystals.

Analysis and design of an annular-array MPT for the efficient generation of omnidirectional shear-horizontal waves in plates

Despite the fact that omnidirectional shear-horizontal (SH) waves have recently received much attention, there is no systematic design method with which to develop the corresponding transducers with enhanced output and power concentration levels at a target frequency. Here, we propose a method which can be used to design an optimal annular-array magnetostrictive patch transducer (MPT) that fulfills the above-mentioned objectives. The proposed transducer consists of optimally configured multiple magnetostrictive patches, consistently placed permanent magnets, and toroid coils. For the design, the transducer output signals are theoretically predicted using Green’s function of guided waves in a plate and the analysis results are then used to develop new high-power annular-array MPTs generating omnidirectional SH waves in a plate. The validity of the analysis and the effectiveness of the design method were confirmed with numerical simulations and pitch-catch wave experiments performed on an aluminum plate. In the experiments, the mode selectivity and omnidirectivity of the designed transducer were also checked. While the proposed method is mainly developed for MPTs, it should be equally useful for the design of similar annular-type piezoelectric and electromagnetic acoustic guided wave transducers.

Unidirectional focusing of horizontally polarized shear elastic waves electromagnetic acoustic transducers for plate inspection

The ultrasonic guided wave testing method is very effective in monitoring the safety of complex structures. The fundamental shear horizontal (SH) wave mode has the advantage that the propagation velocity does not change with the frequency. However, accurately recognizing the ultrasonic signal is difficult due to the SH guided wave’s bidirectional propagation characteristics generated by the Lorentz force mechanism. Therefore, it is necessary to achieve unidirectional focusing of Lorentz force-generated SH guided waves. A newly designed SH guided wave electromagnetic acoustic transducer (EMAT) is proposed with an interlaced periodic permanent magnet (PPM) and AC coils of different phases. A 3D model based on the electromagnetic mode and the solid mechanics mode using COMSOL software is calculated and compared with the bidirectional focusing EMATs. The results show that there are many influencing factors in the structural design of the transducers, and the focal radius and the angle of the individual PPMs are discussed in this work. The results indicate that the new unidirectional EMAT shows superiority in many cases, and the decrease of the focal radius with a suitable aperture angle will increase the focusing intensity of the signal.

Shear horizontal wave propagation along a periodic metal grating surface of a magneto-electro-elastic substrate

This paper analyzes shear horizontal (SH) waves propagating in thin metal strips deposited periodically onto the surface of a magneto-electro-elastic (MEE) substrate. The MEE substrate is assumed to be a transversely isotropic crystal with 6 mm symmetry or a hexagonal (6 mm) crystal. A field analysis method, which is based on the Bloch–Floquet theory and the coupled equations of wave motion, is employed to derive the dispersion equations and wave mode shapes. Numerical examples are presented for an MEE composite (PZT4/CoFe2O4) and an aluminum (Al) strip. For comparison, different constituent ratios of PZT4/CoFe2O4 are considered. The effect of the ratios of strip height and width to grating periodicity on frequencies, phase velocities, as well as wave mode shapes is discussed in detail. The results show that there is a bandgap at the resonance condition when the grating periodicity matches the wavelength of the SH surface wave. This metal grating surface can trap SH surface waves by slowing the SH waves. The wave mode shapes indicate that the SH surface waves are trapped mainly on these metal strips. As the ratio of strip height to grating periodicity increases, the trapping effect is more pronounced and the gap becomes wider. The ratio of strip width to grating periodicity significantly affects the behavior of SH surface waves. The present results are relevant in the application of MEE surface acoustic wave resonators.