Effect of initial stress on Love waves in a piezoelectric structure carrying a functionally graded material layer

The effect of initial stress on the propagation behavior of Love waves in a piezoelectric half-space of polarized ceramics carrying a functionally graded material (FGM) layer is analytically investigated in this paper from the three-dimensional equations of linear piezoelectricity. The analytical solutions are obtained for the dispersion relations of Love wave propagating in this kind of structure with initial stress for both electrical open case and electrical short case, respectively. One numerical example is given to graphically illustrate the effect of initial stress on dispersive curve, phase velocity and electromechanical coupling factor of the Love wave propagation. The results reported here are meaningful for the design of surface acoustic wave (SAW) devices with high performance.     

Love waves in functionally graded piezoelectric materials by stiffness matrix method

A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO₂, the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour.     

Love waves in layered flexoelectric structures

Abstract

In this paper, the flexoelectric effect on Love waves propagating in a structure with a nanoscale piezoelectric guiding layer deposited on an isotropic elastic substrate is analytically investigated. Transcendental complex dispersion equations are obtained and solved numerically which are corresponding to the electrically open and short conditions at the free surface. A detailed discussion about the dispersion relations of the fundamental mode is subsequently presented. The results indicate that flexoelectricity has a substantial effect on Love wave propagation. The presence of flexoelectricity leads to a complex phase velocity with a negative/positive imaginary part, which means Love waves attenuate/grow over time. In addition, the phase velocity dispersion relations depend greatly on the thickness and flexoelectric coefficients of the guiding layer. The current work is the first attempt to explore the flexoelectric effect on the propagation characteristics of surface acoustic waves (SAWs). And the results would be beneficial to achieve a better performance of SAW devices.     

Love-type waves in functionally graded piezoelectric material (FGPM) sandwiched between initially stressed layer and elastic substrate

This paper investigates the propagation behavior of Love-type surface waves in three-layered composite structure with initial stress. The composite structure has been taken in such a way that a functionally graded piezoelectric material (FGPM) layer is bonded between initially stressed piezoelectric upper layer and an elastic substrate. Using the method of separation of variables, frequency equation for the considered wave has been established in the form of determinant for electrical open and short cases on free surface. The bisection method iteration technique has been used to find the roots of the dispersion relations which give the modes for electrical open and short cases. The effects of gradient variation of material constant and initial stress on the phase velocity of surface waves are discussed. Dependence of thickness on each parameter of the study has been shown explicitly. Study has been also done to show the existence of cut-off frequency. Graphical representation has been done to exhibit the findings. The obtained results are significant for the investigation and characterization of Love-type waves in FGPM-layered media.     

Theoretical validation on the existence of two transverse surface waves in piezoelectric/elastic layered structures

In this paper, we analytically study the dispersion behavior of transverse surface waves in a piezoelectric coupled solid consisting of a transversely isotropic piezoelectric ceramic layer and an isotropic metal or dielectric substrate. This study is a revisit to the stiffened Love wave propagation done previously. Closed-form dispersion equations are obtained in a very simple mathematical form for both electrically open and shorted cases. From the viewpoint of physical situation, two transverse surface waves (i.e., the stiffened Love wave and the FDLW-type wave) are separately found in a PZT-4/steel system and a PZT-4/zinc system. All the observed dispersion curves are theoretically validated through the discussion on the limit values of phase velocity using the obtained dispersion equations. Those validation and discussion give rise to a deeper understanding on the existence of transverse surface waves in such piezoelectric coupled structures. The results can be used as a benchmark for the study of the wave propagation in the piezoelectric coupled structures and are significant in the design of wave propagation in the piezoelectric coupled structures as well.     

The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates

This study analytically investigates the propagation of shear waves (SH waves) in a coupled plate consisting of a piezoelectric layer and an elastic layer with initial stress. The piezoelectric material is polarized in z-axis direction and perfectly bonded to an elastic layer. The mechanical displacement and electrical potential function are derived for the piezoelectric coupled plates by solving the electromechanical field equations. The effects of the thickness ratio and the initial stress on the dispersion relations and the phase and group velocities are obtained for electrically open and mechanically free situations. The numerical examples are provided to illustrate graphically the variations of the phase and group velocities versus the wave number for the different layers comparatively. It is seen that the phase velocity of SH waves decreases with the increase of the magnitude of the initial compression stress, while it increases with the increase of the magnitude of the initial tensile stress. The initial stress has a great effect on the propagation of SH waves with the decrease of the thickness ratio. This research is theoretically useful for the design of surface acoustic wave (SAW) devices with high performance.     

Love wave propagation in functionally graded piezoelectric material layer

An exact approach is used to investigate Love waves in functionally graded piezoelectric material (FGPM) layer bonded to a semi-infinite homogeneous solid. The piezoelectric material is polarized in z-axis direction and the material properties change gradually with the thickness of the layer. We here assume that all material properties of the piezoelectric layer have the same exponential function distribution along the x-axis direction. The analytical solutions of dispersion relations are obtained for electrically open or short circuit conditions. The effects of the gradient variation of material constants on the phase velocity, the group velocity, and the coupled electromechanical factor are discussed in detail. The displacement, electric potential, and stress distributions along thickness of the graded layer are calculated and plotted. Numerical examples indicate that appropriate gradient distributing of the material properties make Love waves to propagate along the surface of the piezoelectric layer, or a bigger electromechanical coupling factor can be obtained, which is in favor of acquiring a better performance in surface acoustic wave (SAW) devices.     

Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure

Based on the theories of nonlinear continuum mechanics, piezoelectricity and elastic waves in solids, theoretical analysis of Bleustein-Gulyaev surface acoustic wave propagation in a prestressed layered piezoelectric structure are described. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO(3) except that they are polarized in opposite directions. It is found that an almost linear behavior of the relative change in phase velocity versus the initial stress is obtained for both surface electrically free and shorted cases. Potential applications in the design of acoustic wave devices are suggested.     

Propagation of SH-waves in two anisotropic layers bonded to an isotropic half-space under gravity

This study reports a theoretical investigation of the propagation of SH-wave in a piezoelectric layer superimposed on a self-reinforced layer overlying an isotropic gravitational half-space. The expressions of the dispersion relation of SH-wave have been established for electrically open and electrically short conditions in closed form. For the purpose of numerical computation, lithium niobate piezoelectric material has been considered. The dispersion curves have been depicted graphically and the prominent impacts of piezoelectric constant, dielectric constant, reinforced parameter, width ratio, and Biot’s gravity parameter on the phase velocity of SH-wave have been unraveled for both the electrical conditions. As a special case of the problem, it is found that the obtained dispersion relation concurs with classical Love wave equation for both the electrical conditions. Moreover, some important peculiarities have also been traced out through numerical computations for both the electrical cases.     

Love wave propagation in piezoelectric layered structure with dissipation

We investigate analytically the effect of the viscous dissipation of piezoelectric material on the dispersive and attenuated characteristics of Love wave propagation in a layered structure, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of the viscous coefficient on the phase velocity of Love waves and attenuation are presented and discussed in detail. The analytical method and the results can be useful for the design of the resonators and sensors.     

Transverse surface waves in a layered structure with a functionally graded piezoelectric substrate and a hard dielectric layer

As to an ideally layered structure with a functionally graded piezoelectric substrate (material parameters change continuously along the thickness direction) and a hard dielectric layer, the existence and propagation behavior of transverse surface waves is studied by analytical technique. The dispersion equations for the existence of the transverse surface waves with respect to phase velocity are obtained for electrically open and short circuit conditions, respectively. A detailed investigation of the effect of gradient coefficient on dispersion relation, electromechanical coupling factor and penetration depth is carried out. It is found by numerical examples that adjusting gradient coefficient makes the electromechanical coupling factor of the transverse surface waves achieve quite high values at some appropriate ratio values of the layer thickness to the wavelength, and at the same time, the penetration depth can be reduced to the same order as the wavelength.     

Effect of periodic corrugation,reinforcement, heterogeneity and initial stress on Love wave propagation

This paper investigates the impact of corrugated boundary surfaces, reinforcement on the propagation of Love-type wave in prestressed corrugated heterogeneous fiber-reinforced layer resting over a void pores half-space. The heterogeneity in the upper corrugated layer is caused due to exponential variation in the elastic constants with respect to the space variable pointing positively downwards. The dispersion equation in the complex form has been derived using method of separation of variables. The real and imaginary parts of the complex dispersion equation were separated and found in well agreement with the classical Love wave equation. Also, the attenuation of the Love waves has been discussed. The study reveals that such a medium transmits two fronts of Love waves. The first front depends upon the change in volume fraction of the pores and the second front depends upon the modulus of rigidity of the elastic matrix of the medium. The substantial influence of corrugation parameters, reinforcement, undulatory parameter, initial stress, heterogeneity parameter and position parameter on the phase velocity, and attenuation of Love-type wave have been observed and depicted by means of graph. It has been observed that the phase velocity decreases with the increase in initial stress parameters, heterogeneity, and reinforcement in upper layer.     

The piezoelectric and piezomagnetic effect on the surface wave velocity of magneto-electro-elastic solids

The direction dependence of surface wave speed and the influence of electrically and magnetically short/open circuit conditions are investigated in this paper. First, the elastic, piezoelectric and piezomagnetic coefficients in the considered ordinate system are obtained by Bond transformation from that in the crystal axis ordinate system. Then, the secular equation which surface wave speed satisfies is derived from the free traction condition on the surface of half-space with consideration of electrically and magnetically short/open circuit conditions. Some numerical examples are given. The direction dependence of surface wave speed and the influence of short and open circuit conditions are shown graphically.     

SH surface acoustic wave propagation in a cylindrically layered piezomagnetic/piezoelectric structure

SH surface acoustic wave (SH-SAW) propagation in a cylindrically layered magneto-electro-elastic structure is investigated analytically, where a piezomagnetic (or piezoelectric) material layer is bonded to a piezoelectric (or piezomagnetic) substrate. By means of transformation, the governing equations of the coupled waves are reduced to Bessel equation and Laplace equation. The boundary conditions imply that the displacements, shear stresses, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The magneto-electrically open and shorted conditions at cylindrical surface are taken to solve the problem. The phase velocity is numerically calculated for different thickness of the layer and wavenumber for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. The effects of magnetic permeability on propagation properties of SH-SAW are discussed in detail. The distributions of displacement, magnetic potential and magneto-electromechanical coupling factor are also figured and discussed.     

乐甫波结冰状态监测的响应机理分析

提出了将冰层进行多孔介质等效方法,对冰层、液体/波导层/压电基底多层乐甫(Love)波导结构建立分层介质模型,利用部分波理论和边界条件精确推导,分析不同状态下的传感响应,求解结冰过程Love波速度及声波衰减的变化,获得结冰过程中的声学传感机制。为了验证理论分析,实验制作了200 MHz的36°LiTaO₃/SiO₂波导结构的Love波器件,并构建模拟环境的试验系统对研制器件进行了实验测试。实验结果表明,利用Love波的工作频率以及插入损耗瞬变这一特征可以实现对结冰状态的准确监测。      

Propagation behavior of two transverse surface waves in a three-layer piezoelectric/piezomagnetic structure

Propagation of transverse surface waves in a three-layer system consisting of a piezoelectric/piezomagnetic (PE/PM) bi-layer bonded on an elastic half-space is theoretically investigated in this paper. Dispersion relations and mode shapes for transverse surface waves are obtained in closed form under electrically open and shorted boundary conditions at the upper surface. Two transverse surface waves related both to Love-type wave and Bleustein–Gulyaev (B–G) type wave propagating in corresponding three-layer structure are discussed through numerically solving the derived dispersion equation. The results show that Love-type wave possesses the property of multiple modes, it can exist all of the values of wavenumber for every selected thickness ratios regardless of the electrical boundary conditions. The presence of PM interlayer makes the phase velocity of Love-type wave decrease. There exist two modes allowing the propagation of B–G type wave under electrically shorted circuit, while only one mode appears in the case of electrically open circuit. The modes of B–G type wave are combinations of partly normal dispersion and partly anomalous dispersion whether the electrically open or shorted. The existence range of mode for electrically open case is greatly related to the thickness ratios, with the thickness of PM interlayer increasing the wavenumber range for existence of B–G type wave quickly shortened. When the thickness ratio is large enough, the wavenumber range of the second mode for electrically shorted circuit is extremely narrow which can be used to remove as an undesired mode. The propagation behaviors and mode shapes of transverse surface waves can be regulated by the modification of the thickness of PM interlayer. The obtained results provide a theoretical prediction and basis for applications of PE–PM composites and acoustic wave devices.     

Effects of initial compression stress on wave propagation in carbon nanotubes

An analytical method to investigate wave propagation in single- and double- walled carbon nanotubes under initial compression stress is presented. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The governing equations are derived based on Flügge equations of motion. Frequency equations of wave propagation in single and double wall carbon nanotubes are described through the effects of initial compression stress and van der Waals force. To show the effects of Initial compression stress on the wave propagation in nanotubes, the symmetrical mode can be analyzed based on the present elastic continuum model. It is shown that the wave speed are sensitive to the compression stress especially for the lower frequencies.     

New approach to the excitation of plate waves for piezoelectric thick-film devices

A method is presented for exciting the propagation of plate waves in elastic guides. It is implemented in a device whose minimum working structure consists of a non-piezoelectric plane guide and two piezoelectric transducers operating as a generator and detector. The device is entirely in accordance with thick-film technology standard procedures. Both transducers are composed of a PZT ferroelectric layer deposited on a ceramic substrate and a suitable system of three coplanar metal electrodes placed inside the same layer. Beside setting the wavelength of propagation, the electrode system promotes piezoelectric deformations parallel to the substrate simultaneously contracting and extending contiguous active regions in the layer. Pure shear stresses are then induced on the involved guide surface, alternately distributed, with the spatial periodicity of the wave that will propagate in the guide. The propagation of several kinds of guided waves is possible so the selection of the one that meets a specific device design best is allowed.This work describes the design, realization and operation of a prototype structure consisting of an alumina plate guide and two pairs of piezoelectric thick-film transducers realized on it. The results related to the propagation of symmetric and asymmetric Lamb modes are reported. Moreover, the potential of the method is highlighted, emphasizing its effectiveness, easy implementation and application in the development of devices for the sensing and non-destructive testing areas.     

Effects of the imperfect interface and piezoelectric/piezomagnetic stiffening on the SH wave in a multiferroic composite

Studied in the present work is the propagation of SH wave in a cylindrically multiferroic composite consisting of a piezoelectric layer and a piezomagnetic central cylinder. It is assumed that the interface in the composite is damaged mechanically, magnetically or electrically. The dispersion relations of SH wave are obtained for two kinds of electric-magnetic boundary conditions at the free surface, and then the phase velocity is calculated numerically. Parametric studies on the phase velocity yield three main conclusions. (a) The mechanical imperfection may remarkably reduce the phase velocity, depending on the combination of the values of the wavenumber and the thickness ratio. (b) The magneto-electrical imperfection has no obvious effect on the phase velocity in any cases. (c) The piezoelectric and piezomagnetic stiffening can increase the phase velocity.     

Frequency separation of surface acoustic waves in layered structures with acoustic metamaterials

We show theoretically that in elastic layered structures containing an upper layer of smoothly varied thickness and a substrate of a highly dispersive metametarial it is possible to significantly enhance spatial frequency separation of surface acoustic waves. Theory of Love surface acoustic waves propagation in waveguides with varied thickness, taking into account mutual modes coupling, is built. Appropriate structure of metamatererial with resonant frequency dependence of material parameters, making frequency separation effective, is provided. Efficiency of spatial frequency separation and modes coupling is calculated for various metamaterial parameters and wave frequencies.