SH wave propagation in a cylindrically layered piezoelectric structure with initial stress

Summary SH wave propagation in a cylindrically layered piezoelectric structure with initial stress is investigated analytically. By means of transformation, the governing equations of the coupled waves are reduced to Bessel and Laplace equations. 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. The electrically open and short conditions at the cylindrical surface are applied to solve the problem. The phase velocity is numerically calculated for the electrically open and short cases, respectively, for different wavenumber and thickness of the layer. The effect of the initial stress on the phase velocity and the electromechanical coupling factor are discussed in detail for piezoelectric ceramics PZT-5H. We find that the initial stress has an important effect on the SH wave propagation in the cylindrically layered piezoelectric structures. The results also show that the ratio of the layer thickness to the wavelength has a remarkable effect on the SH wave phase velocity and electromechanical coupling factor.     

Love wave propagation in layered magneto-electro-elastic structures with initial stress

Summary An analytical approach is taken to investigate Love wave propagation in layered magneto-electro-elastic structures with initial stress, where a piezomagnetic (piezoelectric) material thin layer is bonded to a semi-infinite piezoelectric (piezomagnetic) substrate. The magneto-electrically open and short conditions are applied to solve the problem. The phase velocity of the Love wave is numerically calculated for the magneto-electrically open and short cases, respectively. The effect of the initial stress on the phase velocity and the magneto-electromechanical coupling factor are studied in detail for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. We find that the initial stress has an important effect on the Love wave propagation in layered piezomagnetic/piezoelectric structures.     

Bulk wave propagation in layered piezomagnetic/piezoelectric plates with initial stresses or interface imperfections

Bulk wave propagation in laminated piezomagnetic/piezoelectric plates with initial stresses and imperfect interface is investigated using the state space approach. Either electrically and magnetically open or shorted conditions on the top and bottom surfaces are considered. The phase velocity and frequency spectra of the wave are numerically calculated for various electric and magnetic conditions, and normalized modes are also analyzed. Although numerical results do indicate that the initial compressive stress can reduce the phase velocity of the wave propagating in a layered multiferroic structure, the effect is not as obvious as that reported in literature where the initial stresses were taken far beyond the strength of real materials. While the imperfect interface affect the frequency spectra much greater than initial stresses, because imperfection decreases the structural stiffness.     

非理想界面功能梯度压电/压磁层状半空间结构中的SH波

研究非理想界面下功能梯度压电/压磁层状半空间结构中SH波的传播特性。界面性能由“弹簧”模型表征, 假设功能梯度压电层材料性能沿层厚度方向指数变化, 其表面为电学开路。推导了频散方程, 并结合数值算例分析了界面性能、功能梯度压电层的梯度变化和厚度对相速度的影响。研究结果对功能梯度压电/压磁复合材料在声波器件中的应用提供了理论依据。     

Interface waves along an anisotropic imperfect interface between anisotropic solids

First and second order asymptotic boundary conditions are introduced to model a thin anisotropic layer between two generally anisotropic solids. Such boundary conditions can be used to describe wave interaction with a solid-solid imperfect anisotropic interface. The wave solutions for the second order boundary conditions satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. They couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic substrates. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This model determines the transfer matrix which includes interfacial stiffness and inertial and coupling terms. The present results are a generalization of previous work valid for either an isotropic viscoelastic layer or an orthotropic layer with a plane of symmetry coinciding with the wave incident plane. The problem of localization of interface waves is considered. It is shown that the conditions for the existence of such interface waves are less restrictive than those for Stoneley waves. The results are illustrated by calculation of the interface wave velocity as a function of normalized layer thickness and angle of propagation. The applicability of the asymptotic boundary conditions is analyzed by comparison with an exact solution for an interfacial anisotropic layer. It is shown that the asymptotic boundary conditions are applicable not only for small thickness-to-wavelength ratios, but for much broader frequency ranges than one might expect. The existence of symmetric and SH-type interface waves is also discussed.     

Shear horizontal (SH) waves propagating in piezoelectric–piezomagnetic bilayer system with an imperfect interface

This work considers the propagation of shear horizontal (SH) waves in a bilayer system consisting of a piezoelectric (PE) layer and a piezomagnetic (PM) substrate. The interface between the PE layer and the PM substrate is imperfectly bonded. The surfaces of the bilayer system are free of traction, electrically shorted or open and magnetically open or shorted. The exact dispersion equations are derived. The numerical examples are given to illustrate the effects of the electromagnetic boundary conditions, the imperfect interface, the different PE layers and the thickness ratio on the dispersion behaviors. It is found that (a) the electrical boundary conditions dominate the propagation characteristics of SH waves; (b) the imperfect bonding lowers the phase velocities; (c) the thickness ratio and the properties of PE layers have a significant effect on the dispersion behaviors. The obtained results provide a predictable and theoretical basis for applications of PE–PM composites to acoustic wave devices.     

间隙波在功能梯度压电板和压电半空间结构中的传播

研究了间隙波在功能梯度压电板和压电半空间结构中的传播性质.功能梯度压电板的材料性能沿x2方向呈指数变化,首先推导了间隙波传播时的解析解,利用界面条件得到了间隙波的频散方程,基于推导的频散方程,结合数值算例分析了功能梯度压电材料的梯度、压电层厚度以及材料性能对间隙波相速度的影响,研究结果对功能梯度压电材料的覆层结构在声波器件中的应用具有重要的参考价值.     

Rayleigh-Type Wave in A Rotated Piezoelectric Crystal Imperfectly Bonded on a Dielectric Substrate

Propagation characteristics of Rayleigh-type wave in a piezoelectric layered system are theoretically investigated. The piezoelectric layer is considered as a cubic crystal with finite thickness rotated about Y-axis and is imperfectly bonded onto a semi-infinite dielectric substrate. The imperfect interface between the two constituents is assumed to be mechanically compliant and dielectrically weakly conducting. The exact dispersion relations for electrically open or shorted boundary conditions are obtained. The numerical results show that the phase velocity of Rayleigh-type wave is symmetric with respect to the cut orientation of 45。 and can achieve the maximum propagation speed in this orientation. The mechanical imperfection plays an important role in the dispersion relations, further the normal imperfection can produce a significant reduction of phase velocity comparing with the tangential imperfection. Comparing with the mechanical imperfection the electrical imperfection makes a relatively small reduction of phase velocity of Rayleigh-type wave. The obtained results can provide some fundamentals for understanding of piezoelectric semiconductor and for design and application of piezoelectric surface acoustic wave devices.     

压电/压磁双材料板中弹性波的传播特性

研究由横观各向同性压电和压磁层构成的双材料板中弹性波的传播特性。板的表面是机械自由的,而承受4种形式的电磁边界条件,压电层和压磁层之间是完好连接的。首先采用部分波分析法推导了压电和压磁耦合方程的一般解,然后利用边界和界面条件得到了行列式形式的频散方程。基于推导的频散方程,通过计算CoFe2O4压磁层与BaTiO3、PZT-5A、PZT-2和PZT-4四种压电层构成的双材料板中弹性波的传播速度,揭示了电磁边界条件、压电层和压磁层的厚度比及压电材料性能对频散特性的影响。     

Acoustoelastic effect in stressed heterostructures

Mechanical stresses influence the phase velocity of acoustic waves, known as the AE (acoustoelastic) effect. In order to calculate the AE effect of biaxially stressed layered systems, we extended the transfer matrix method for acoustic wave propagation by considering the change of the density, the influence of residual stress, and the modification of the elastic stiffness tensor by residual strain and by third-order constants. The generalized method is applied to the calculation of the angular dispersion of the AE effect for transverse bulk modes and surface acoustic waves on Ge(001). Our calculations reveal that the AE effect significantly depends on the propagation direction and can even change sign. The maximal velocity change occurs for transversally polarized waves propagating parallel to the [110] direction. For the layered Ge/Si(001) system, the AE effect is investigated for Love modes propagating in the [100] and [110] directions. The AE effect increases rapidly with increasing layer thickness and almost reaches its maximal value when the wave still penetrates into the unstressed substrate     

Love waves propagation in a piezoelectric layered structure with initial stresses

Summary. The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures.     

Analysis of piezoelectric boundary acoustic wave in Cu electrode/Y-cut X-propagating LiNbO3 substrate structure partially covered with SiO2

This paper describes the existence of piezoelectric boundary acoustic wave (PBAW) propagating in a Cu electrode/Y-cut X-propagating (YX) LiNbO(3) substrate structure partially covered with a SiO2 layer. In the analysis, two types of structures are taken into consideration: one is the so-called slotted structure with SiO2 pillars placed in the grating slots; the other is the so-called topped structure with SiO(2) pillars placed on the top of grating electrodes. The top surface could be fully covered with an additional layer (like epoxy) to bridge the grating slots for encapsulation. Results show that SH-type PBAW begins to propagate in the slotted structure when the SiO(2) thickness exceeds 0.3 wavelength. Strong electromechanical coupling factor K(2) of 21%, and temperature coefficient of velocity (TCV) of -33 ppm/°C are obtained. In the topped structure, on the other hand, the boundary acoustic wave mode is not supported. Instead, the thickness resonance modes in the SiO2 pillar do exist. Comparison of the obtained results with those in the structure fully covered with the SiO(2) layer indicates that, as for the PBAW mode, the slotted structure offers improved K(2) but with worse TCV compared with the fully covered SiO(2) structure.     

Shear-horizontal surface waves on piezoelectric ceramics with depolarized surface layer

Theoretical analysis and numerical results describing the propagation of SH (shear-horizontal) surface waves on piezoelectric ceramics with a depolarized surface layer are described. SH surface waves propagating in piezoelectric ceramics with a depolarized surface layer are shown to be a mixture of the Bleustein-Gulyaev surface wave, electrical potential, and the Love surface-wave mechanical displacement. Depolarization of the surface layer in piezoelectric ceramics produces strong dispersion and a multimode structure of the SH surface wave. The penetration depth of the SH surface waves propagating on an electrically free surface of a piezoelectric ceramic with a depolarized surface layer can be significantly smaller than that of the Bleustein-Gulyaev surface waves propagating on a free piezoelectric half-space. It is concluded that piezoelectric ceramics with a depolarized surface layer can be used in hybrid piezoelectric semiconductor convolvers of reduced size.     

功能梯度压电双材料板中厚度-扭曲波的传播

分析了厚度-扭曲波在无限大功能梯度压电双材料板中的传播性能,板的上表面和下表面是机械自由和电学开路的,材料常数在厚度方向按指数规律变化。首先推导了满足控制方程和边界条件的电弹场,然后利用界面条件得到了厚度-扭曲波传播所应满足的关系。通过算例表明了材料梯度变化对厚度-扭曲波传播性能的影响,结果对功能梯度压电材料在声波器件中应用有参考价值。     

压电弹性层合梁-板结构中SH波的传播

建立了压电层合梁-板结构的压电-弹性动力学基本方程式，在给定压电层合梁-板结构形式和波传播方向的情况下，对基本方程式进行了简化；利用连续性条件和边界条件，建立了波传播的特征方程式，并对波动方程式进行求解；得到了前三阶频散关系曲线。通过实例数值计算，讨论了弹性层、压电层的厚度比与频散关系的影响，得出了SH波在压电层合梁-板结构中传播的基本特性。     

Effect of a ferroelectric inversion layer on the temperature characteristics of SH-Type surface acoustic waves on 36 degrees Y-X LiTaO (3) substrates

The temperature coefficient of delay of the SH-type surface acoustic wave on 36 degrees Y-X LiTaO(3) substrates with a ferroelectric inversion layer is theoretically analyzed and it is shown that the temperature characteristics can be improved by an electric-field short-circuiting effect of the domain boundary. The experimental results of the temperature coefficient of delay agree well with the theoretical. The minimum value of measured temperature coefficients of delay is 12.6 ppm/ degrees C for the metallized surface case, which is about one-third of that in a 36 degrees Y-X substrate with no inversion layer. Experimental results on the phase velocity and the electromechanical coupling factor of the SH-type surface acoustic wave are also presented and compared with the theoretical.     

Dispersion relations for SH-wave propagation in periodic piezoelectric composite layered structures

Propagation behavior of horizontally polarized shear waves (SH-waves) in a periodic piezoelectric-polymeric layered structure is taken into account. The layered structures are consisted of piezoelectric thin films bonded perfectly with polymeric thin films alternately. The phase velocity equations of SH-waves propagation in the periodic layered piezoelectric structure are obtained for the cases of wave propagation in the direction normal to the interface and along the interface, respectively. Filter effect of this kind of structure and the effects of volume fraction and shear modulus ratio of piezoelectric layer to polymeric layer on the phase velocity are discussed in detail, respectively. One set of piezoelectric thin film--polymeric thin film multilayer system (PZT-5H piezoelectric ceramics--polythene) is chosen to show the numerical simulation, basic properties of SH-waves propagation in this particular structure are revealed.     

Study on SH-SAW in imperfectly bonded piezoelectric structures loaded with viscous liquid

We analytically investigate shear horizontal surface acoustic wave (SH-SAW) propagation in layered piezoelectric structures loaded with viscous liquid, which involves a thin piezoelectric layer imperfectly bonded to an unbounded elastic substrate. The coupling wave equations are obtained based on the linear piezoelectric theory. The governing equations are solved by means of the analytical method with consideration of electrically open and shorted cases, respectively. The dispersive relations are obtained, and the effects of the imperfect constant on the properties of waves are presented and discussed. From the numerical results, we can find that the phase velocity decreases with the increase of the interface parameter n, and for a specified viscosity, the attenuation increases with the interface parameter. The results show that the effects of the imperfect constant on the properties of SH-SAW are remarkable.     

液体-压电晶片界面上电边界条件对兰姆波激发的影响

本文对液体-压电晶片结构中,不同电边界条件下叉指换能器所激发的兰姆波传播特性进行了分析研究,给出了不同电边界条件下兰姆波的相速度、叉指换能器激发兰姆波的机电耦合系数与压电晶片的归一化厚度、晶体切向之间的关系曲线,为实际设计中电边界条件的正确选择提供了理论基础。     

A unified formalism using effective surface permittivity to study acoustic waves in various anisotropic and piezoelectric multilayers

A unified formalism is presented that uses the effective surface permittivity (ESP) to study surface acoustic waves (SAW) in layered substrates and guided waves in layered plates. Based on known mathematical tools, such as ordinary differential equation and transfer matrix, a generalized surface impedance (GSI) concept is developed and exploited to investigate the acoustic propagation in various anisotropic and piezoelectric layered structures. The ESP function, originally defined for the surface of a homogeneous and semi-infinite piezoelectric substrate, is extended to both the top surface of and an interface in a layered half space, as well as to either surface of a finite-thickness plate. General ESP expressions for all mentioned configurations are derived in terms of an equivalent GSI matrix. It is shown that, when using the appropriate GSI matrices, the same form of the ESP expressions applies no matter whether the structure is a homogeneous half space alone or coated with a layered plate or a layered plate alone. GSI matrices are explicitly given in terms of the bulk partial mode solutions for a substrate and via the transfer matrix for a plate. Modified GSI matrices for structures consisting of both a plate and a substrate are also specified. Analytical development is fully detailed to suit program implementation. To illustrate its versatility, the formalism is also applied to two-substrate configurations, allowing one to analyze guided waves in a plate sandwiched between and interfacial waves existing along the boundary of two different media. Numerical examples are given to illustrate the spectrum features that the ESP shows for various structures. Deduced ESP expressions allow one to locate directly all piezoelectrically active waves in any structure including at least one piezoelectric layer. Acoustic modes that are not piezoelectrically active and those in non-piezoelectric materials can be also obtained by using the intermediate results, such as derived GSI matrices.