Shear Horizontal Wave Propagation Research Articles

Interfacial waves in a piezoelectric/piezomagnetic/piezoelectric structure with magneto-electro-mechanical imperfect interfaces

In this paper, we study the propagation of Shear Horizontal (SH) waves in the interfaces of a piezoelec-tric/piezomagnetic/piezoelectric (PiezoE/ PiezoM/ PiezoE) structure with a magnetical, imperfect magnetic, electric, and mechanical condition at interfaces. The inclusion of magnetical imperfections produced several new results, such as a general dispersion relation and expressions for some limit cases, which were not re-ported previously in the literature, predicting the existence of interfacial waves. Employing numerical calcu-lations, dispersion curves for this kind of structure are presented for the first time. It can be shown that the magnetical imperfection interface influences the dispersion curves. Our results show that especially magnetic imperfections have a significant influence on the dispersion curves.

Effects of physical parameters on shear wave in a porous piezoelectric model with imperfect interface

This study investigates the impact of interfacial imperfection on shear horizontal wave propagation in a microstructural coupled stress half-space beneath a porous piezoelectric layer adjacent to air. The validity of dispersion relations is shown by deriving special cases and comparing them with the classical dispersion relation of Love wave. Furthermore, a comparative analysis has been conducted to analyze the effect of various parameters on the phase velocity of shear wave by considering perfect and imperfect interfaces under electrically open and short conditions. The findings provide a theoretical framework for developing and designing underwater acoustic devices for sensing and nondestructive testing.

Rotation effects on propagation of shear horizontal surface waves in piezomagnetic-piezoelectric semiconductor layered structures

In this work, the propagation characteristics of shear horizontal waves in a piezomagnetic and piezoelectric semiconductor layered structure with rotation are studied. The dispersion equation of shear horizontal waves in the rotating multiferroic composite semiconductor is obtained in the framework of coupled field theory including Coriolis and centrifugal forces. By solving the dispersion equation in complex domain, the influence of rotation on the shear horizontal waves is deeply analyzed, and the effects of steady-state carrier concentration and biasing electric field in the presence and absence of rotation are obtained, respectively. Similar to the semiconductor properties, the results show that the rotation will also cause dispersion and attenuation of shear horizontal waves. Besides, the wave speed decreases with the increase of the angular rate and the frequency shift occurs. The rotation sensitivity at long wavelengths near the surface is greater than those at short wavelengths deep into the half-space. Importantly, the increase in wave speed and amplitude gain can be achieved by applying an appropriate biasing electric field regardless of rotation or non-rotation. Specially, several critical points such as attenuation from large to small with rotation, wave speed from decrease to increase and wave amplitude from attenuation to gain in the biasing electric field are obtained. The results could be helpful for the design of surface acoustic wave gyroscopes and piezoelectric semiconductor devices related to magnetic fields.

Band gap of shear horizontal waves for one-dimensional phononic crystals with chiral materials.

Extensive applications of chiral lattice structures in the field of acoustic wave manipulation and vibration modulation show the effectiveness of chirality route to the design of phononic crystals. However, how and to what extent the material chirality affects the band gap properties of phononic crystals remains unclear. In this study, one-dimensional phononic crystals made of chiral materials is proposed, and a theoretical model of shear horizontal (SH) wave propagation in the chiral phononic crystals is developed based on the noncentrosymmetric micropolar elasticity theory. Through the transfer matrix method, the dispersion relationship of SH wave propagation is obtained and the effects of material chirality on the band-gap properties are investigated. Our work demonstrates that the change of material chirality can significantly affect the dispersion relationship of phononic crystals, leading to the wide band gap and low frequency. In a unit cell, when the chiral coefficients of the two parts have opposite signs but the same magnitude and the chiral directions are consistent with the vibrational direction, it is the most favorable for the phononic crystals to achieve the lowest frequency and widest band gap. This study suggests that the material chirality can be harnessed to effectively tune the band-gap properties of phononic crystals. The present study provides insight for the chirality route to the design of phononic crystals.

Surface effects on wave propagation in piezoelectric–piezomagnetic loosely bonded bilayer system using nonlocal theory of elasticity

This study investigates nonlocal and surface effects on the dispersion behaviors of Shear horizontal (SH) waves in piezoelectric(PE)-piezomagnetic(PM) bilayer systems. The interface between these two layers is imperfectly bonded. The general governing equations are derived from the nonlocal magnetoelectroelastic (MEE) theory by adding an inherent length. The G-M model and generalized Young-Laplace equations have been used to incorporate surface effects into the boundary conditions of the bilayer systems. The closed-form dispersion equation is obtained analytically for electrically open and magnetically short conditions. Numerical solutions are utilized to investigate the effects of nonlocal scale parameters and surface parameters on SH surface wave propagation. Contrary to the results of classical theory, the coupling effects of nonlocal small-scale and surface piezoelectricity are more significant than individual effects. Also, it has been observed that the imperfectness parameter across the interface and the thickness ratio of the bilayer significantly affect the phase velocity. Moreover, 2D and 3D plots of the mode shapes of field variables for the propagation of SH waves are presented graphically. These results are validated by conducting analyses excluding nonlocal effects. This allows us to isolate the specific impact of surface effects in the piezoelectric–piezomagnetic bilayer system, drawing connections to existing results and enhancing the robustness of our findings. This study provides valuable insights into complex wave dynamics, helping to optimize the performance and functionality of such smart composites in various engineering applications.

Exact analytical solution for shear horizontal wave propagation through locally periodic structures realized by viscoelastic functionally graded materials

The paper presents a novel comprehensive exact analytical solution for modeling linear shear-horizontal (SH) wave propagation in an isotropic inhomogeneous layer made of functionally graded material, using local Heun functions. The layer is a composite of two materials with varying properties represented by spatial variations following the square of the sine function. The Voigt–Kelvin model is used to account for material losses. The study focuses on SH waves incident at a specific angle and employs the wave splitting technique to analyze forward and backward waves, facilitating the computation of reflection and transmission coefficients at any point in the inhomogeneous structure. The proposed solution utilizes the periodic nature of material functions and employs the Floquet–Bloch theory to derive an exact analytical solution. This approach is particularly suited for cases where SH waves encounter locally periodic functionally graded material. A Riccati equation-based verification is conducted to compare the frequency-dependent modulus of the reflection coefficient obtained from the analytical solution with numerically solved results. The presented work provides a comprehensive and versatile analytical solution for studying linear SH wave propagation in locally inhomogeneous isotropic layers, contributing to the theoretical understanding of elastic wave fields and practical applications.

Electromagnetic Ultrasonic Shear-Horizontal Wave to Detect Corrosion Defect of Flat Steel for Grounding Device of Transmission Pole Tower

Detecting defects in grounded flat steel is essential for ensuring the safety and reliability of transmission tower grounding devices. However, traditional inspection methods, such as physical excavation and verification, are costly and time-consuming. This paper proposes a corrosion defect detection method for flat steel transmission tower grounding devices based on electromagnetic ultrasonic SH waves. In addition, using commercial software, a three-dimensional finite element simulation model of grounded flat steel with simulated pitting corrosion defects is constructed. The specified displacements applied to multiple surface sources mimic the horizontal shear vibrations generated by the electromagnetic ultrasonic transducer on the surface of the grounded flat steel during actual inspection. A simulation was used to investigate the propagation and attenuation characteristics of shear-horizontal ultrasonic SH0guided waves for simulated corrosion defects with various geometric configurations in grounded flat steel. The simulation investigated the propagation and attenuation characteristics of the SH0 wave in grounded flat steel and the detection of various defects for linear analysis of the results. The simulation results show that the attenuation of the electromagnetic ultrasonic guided wave is small, at only 0.0016 dB/mm, and the displacement amplitude of the echo signal decreases with the increase of the SH0 wave propagation distance. Increasing the depth and length of corrosion defects increases the echo signal amplitude. At the same time, the width of corrosion defects has little effect on the echo amplitude. Finally, a flat steel defect detection experiment was conducted, and the experimental results fit with the simulation to verify the accuracy of the simulation model. This detection method introduces a new idea for the on-site detection and quantitative identification of corrosion defects in grounded flat steel, which has significant reference value and can provide a more effective and economical method for ensuring the safety and dependability of transmission tower grounding devices.

Propagation of shear horizontal (SH) waves in a functionally graded piezoelectric substrate with periodic gratings

Propagation of shear horizontal (SH) waves in a functionally graded piezoelectric substrate with periodic gratings

Shear horizontal wave propagation in multilayered magneto-electro-elastic nanoplates with consideration of surface/interface effects and nonlocal effects

To depict the impact of surface/interface effects and nonlocal effects on Shear Horizontal (SH) waves in Magneto-Electro-Elastic (MEE) coupled nano-structures, a theoretical model is established, motivated by the dual variable and position (DVP) method. The physical mechanism of the material at the nanoscale is distinctive from that of the counterpart material at the macroscale. The above-referenced phenomenon can be mainly attributed to surface effects and nonlocal effects. With the aid of the DVP method, the phase velocity equation concerning surface effects and nonlocal effects is achieved, which shows stable computation in the high-frequency region. After numerical validation, systematic investigations are carried out to illustrate the size-dependent properties of SH waves. It is revealed that SH0 waves, i.e. the fundamental mode of the SH wave, are dispersive, with their phase velocity controlled by the nanoplate thickness if surface/interface effects and nonlocal effects are considered, which is totally different from macro-structures. Additionally, the surface/interface effect increases the structural stiffness so that it enhances the phase velocity, while the non-local constant has the opposite effect. This paper establishes a theoretical model and comes up with some qualitative conclusions that pave the way for the design of the structure of MEE nano-devices.

Size-dependent and piezoelectric effects on SH wave propagation in functionally graded plates

This paper is concerned with the propagation of shear horizontal waves in a functionally graded piezoelectric small-scaled plate. In the context of the modified couple stress theory, the Legendre orthogonal polynomial method is utilized to derive the solutions based on the explicit functionally graded model. Four different electric boundary conditions are considered. The obtained results are compared with those by the global matrix method and the advantages of the polynomial method are indicated. Furthermore, the couple stress effect and piezoelectric effect on the SH waves are investigated. Numerical results indicate that the couple stress and piezoelectric coupling effects on SH propagation are mutually inhibited.

Nonlinear Modes in Shear Horizontal Wave Propagation–Analytical and Numerical Analysis

Nonlinear shear horizontal guided wavefield is investigated analytically in plates. The major focus is on the effect of nonlinear material parameters, excitation frequency, wave number and wave amplitude on nonlinear mode generation. The analytical solution is based on the multiple-scale perturbation method and modal decomposition approach. The approximate analytical solution is validated using the Local Interaction Simulation Approach, implemented for nonlinear shear wave propagation. The results show that the analysed shear horizontal wavefield is distorted by material nonlinearity. The resulting displacement field can be interpreted in a form of nonlinear modes.

Influence of Magnetostriction Induced by the Periodic Permanent Magnet Electromagnetic Acoustic Transducer (PPM EMAT) on Steel.

The periodic permanent magnet electromagnetic acoustic transducer (PPM EMAT) is a sensor that can generate and receive shear horizontal (SH) waves without direct contact with the inspected medium using the Lorentz mechanism. However, the PPM EMAT experiences high signal variance on ferromagnetic steel under specific conditions, such as a change in signal amplitude when the sensor is moved in the direction of SH wave propagation. Magnetostriction effects are hypothesized to be the cause of these anomalous behaviors; the objective of this paper is to determine the relative strengths of the magnetostriction and Lorentz wave generation mechanisms for this type of EMAT on steel. This goal is accomplished through the use of a second EMAT, which induces only magnetostriction (MS-EMAT), to calibrate a novel semi-empirical magnetostriction model. It is found that magnetostriction effects reduce the amplitude of the SH wave generated by this particular PPM EMAT transmitter by an average of 29% over a range of input currents. It is also determined that magnetostriction is significant only in the investigated PPM EMAT transmitter, not the receiver. In terms of practical application, it is shown that the MS-EMAT is less sensitive to changes in the static and dynamic fields than PPM EMATs at specific operating points; this makes the MS-EMAT a viable alternative for nondestructive evaluation despite lower amplitudes.

Comparative study of the piezo-viscous effect of SH wave propagation with irregular and irregular free interfaces in different piezo-electric stratified media

By using the characteristics of two disparate materials (BaTiO ceramic and PZT-5H ceramic) on SiO glass, we have analyzed shear horizontal wave (SH wave) propagation through a piezo-visco-elastic composite medium (PVECM). For the better platform of the originality of the situation, the piezo-visco-elastic medium (PVEM) is taken between two elastic materials. The exact solution of the governing equations is obtained and discussed in detail with the variation of various significant parameters. Irregular and irregular free, both boundary conditions are assumed to find relevant results. The influence of viscosity, piezo-electric parameter and dielectric parameter for irregular and irregular free boundaries on SH-wave propagation through BaTiO ceramic and PZT-5H ceramic materials are shown by some curves. This model contains a huge potential to deal with many commercial and industrial applications. The present investigation has uncovered various crucial results which include for both materials, attenuation coefficient for irregular interface are lower than that of the regular interface. For PZT-5H ceramic material, viscosity, dielectric parameter and piezo-electric parameter have a greater impact on phase velocity and attenuation coefficient in comparison to BaTiO ceramic.

Some comparisons between heterogeneous and homogeneous plates for nonlinear symmetric SH waves in terms of heterogeneous and nonlinear effects

In this article, the propagation of nonlinear shear horizontal waves for some comparisons between the heterogeneous and homogeneous plates is considered. It is assumed that one plate is made of up hyper-elastic, heterogeneous, isotropic, and generalized neo-Hookean materials, and the other consists of hyper-elastic, homogeneous, isotropic, and generalized neo-Hookean materials. Using the known solitary wave solutions, called bright and dark solitary wave solutions, to the nonlinear Schrodinger equation, these comparisons are made in terms of the heterogeneous and nonlinear effects. All numerical results, based on the asymptotic analyses in which the method of multiple scales is used, are graphically presented for the lowest dispersive symmetric branch of both dispersion relations.

Shear-horizontal waves in periodic layered nanostructure with both nonlocal and interface effects

The propagation of shear-horizontal (SH) waves in the periodic layered nanocomposite is investigated by using both the nonlocal integral model and the nonlocal differential model with the interface effect. Based on the transfer matrix method and the Bloch theory, the band structures for SH waves with both vertical and oblique incidences to the structure are obtained. It is found that by choosing appropriate interface parameters, the dispersion curves predicted by the nonlocal differential model with the interface effect can be tuned to be the same as those based on the nonlocal integral model. Thus, by propagating the SH waves vertically and obliquely to the periodic layered nanostructure, we could invert, respectively, the interface mass density and the interface shear modulus, by matching the dispersion curves. Examples are further shown on how to determine the interface mass density and the interface shear modulus in theory.

Mathematical analysis of surface wave transference through imperfect interface in FGPM bedded structure

In the present article, a theoretical investigation has been carried out to analyze the propagation of shear horizontal surface waves (SH-waves) in a structure consisting of a functionally graded piezoelectric material (FGPM) layer lying over an FGPM half-space. The material properties of FGPM layer are assumed to have exponential function distribution along the thickness direction whereas those of FGPM half-space are presumed to have quadratic variation. The interface between the FGPM layer and the FGPM half-space has been considered to be imperfect. At the surface, two cases are considered, electrically open case and electrically short case. Moreover two types of imperfections at the interface are taken into account (one as mechanically compliant and dielectrically weakly conducting and other as mechanically compliant and dielectrically highly conducting). Variable separable method is used for the wave solution. In particular, the solutions for mechanical displacement and electric potential function for FGPM half-space has been obtained in the form of modified Bessel function. The dispersion relation for each case is obtained in determinant form using suitable boundary conditions. Numerical example is given and graphs are plotted. The numerical results show that the surface wave velocity is affected by the layer width, gradient coefficient of the two FGPM media, and the degree of mechanical and dielectrical imperfections at the interface between the covering layer and the substrate. This study finds its application in optimization of SAW devices.

The SH0 wave manipulation in graded stubbed plates and its application to wave focusing and frequency separation

In this study, a methodology to artificially control the propagation of fundamental shear horizontal (SH0) waves in elastic plates is proposed using stubs with spatially graded height, and two novel phenomena, wave focusing and low-pass wave filtering, are realized. As a basis for this, the band structure analysis is carried out for an aluminum plate with hexagonally arranged stubs, and the relationships between the wave velocity, the band gap and the stub height are established. Based on these results, omni-directional SH0 wave-based Luneburg and Maxwell fish-eye lenses, as well as low-pass wave filter, are designed artificially using multiple stubs with spatially graded heights. It is demonstrated that both of the lenses exhibit good focusing ability, with the focusing size smaller than the wavelength. Additionally, they can work with a finite bandwidth around the design frequency. It has also been revealed both in time and frequency domain simulations that the SH0 wave with a lower frequency can travel over a longer distance when it enters the low-pass wave filter, which demonstrates its frequency separation capability.

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.

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.