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.     

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.     

Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent

The theory of generalized thermoelasticity, based on the theory of Green and Lindsay with two relaxation times, is used to deal with a thermoelastic–piezoelectric coupled two-dimensional thermal shock problem of a thick piezoelectric plate of infinite extent by means of the hybrid Laplace transform-finite element method. The generalized thermoelastic–piezoelectric coupled finite element equations are formulated. By using Laplace transform the equations are solved and the solutions of the temperature, displacement and electric potential are obtained in the Laplace transform domain. Then the numerical inversion is carried out to obtain the temperature, displacement and electric potential distributions in the physical domain. The distributions are represented graphically. From the distributions, it can be found the wave type heat propagation in the piezoelectric plate. The heat wavefront moves forward with a finite speed in the piezoelectric plate with the passage of time. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in media.     

An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates

A finite element model for the analysis of fibre-reinforced laminated composite plates embedded and/or surface bonded with piezoelectric layers and subjected to mechanical loading and/or electric potential has been presented in this paper. The proposed model is applicable for the analysis of thin-to-moderately thick plates. No restriction has been imposed on the pattern of variation of the potential across the plate thickness so that the potential can have any value even within the core. As the plates considered here are not too thick, the structural deformation has been modelled by single layer theory where the effect of shear deformation has been taken into account following Mindlin's hypothesis. For the electric potential, layer-wise theory has been applied, as the through-thickness variation of electric potential does not follow any specific pattern. This is the first attempt wherein a combination of single layer theory and layer-wise approach has been used to solve the coupled problem of piezoelectricity in plate bending. Numerical examples have been carried out to study the performance of the proposed approach.     

Effect of An Initial Stress on SH-Type GuidedWaves Propagating in a Piezoelectric Layer Bonded on A Piezomagnetic Substrate

Propagation of SH-type guided waves in a layered structure with an invariant initial stress is studied, where a piezoelectric thin layer is perfectly bonded on a piezomagnetic substrate. Both the layer and the substrate possess transversely isotropic property. The dispersion relations of SH waves are obtained for four kinds of different electro-magnetic boundary conditions. The effects of initial stress, thickness ratio and electro-magnetic boundary conditions on the propagation behaviors are analyzed in detail. The numerical results show that: 1) The positive initial stresses make the phase velocity increasing, while the negative initial stresses decrease the phase velocity; 2) The smaller the thickness ratio of a piezoelectric layer to a piezomagnetic substrate, the larger the phase velocity of SH-type guided wave propagating in the corresponding layered structure; 3) The electrical boundary conditions play a dominant role in the propagating characteristics. Moreover the phase velocities for the electrically shorted surface are smaller than that for the open case. The obtained results are useful for understanding and design of the electromagnetic acoustic wave and microwave devices.     

基于有限元法的周期压电智能梁滤波特性分析

周期结构具有通频和禁频特性,使其在动态载荷的滤波器、具有主动控制功能的结构研究中得到了重要应用。基于Timoshenko梁理论,考虑基梁和压电片的转动惯量和剪切效应,采用有限元法和传递矩阵法推导了波在周期性地粘贴压电片的Timoshenko梁中的传播模型,分析了几何尺寸和材料特性对其频带性质的影响,并与Bernoulli-Euler梁理论得到的结果进行了对比。研究表明,当基梁与压电层厚度比达到40时,禁带带宽减小了54%,因此对于周期结构中的深梁,应舍弃Bernoulli-Euler梁理论而采用Timoshenko梁理论建立的模型;对于不同尺寸和材料特性的压电周期结构,频带性质会有很大不同,可以通过调整结构的参数来改变其频带性质,从而改变波动在结构中的传播特性。     

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.     

Love waves in a smart functionally graded piezoelectric composite structure

The propagation of Love waves in a smart functionally graded piezoelectric structure is analyzed by applying elastic wave theory. There is an additional functionally graded layer between the piezoelectric layer and the substrate in this smart structure. When the piezoelectric and dielectric constants vary individually in a functionally graded layer, the asymptotic solutions of Love waves are obtained by applying the WKB method and solving the fourth order differential equation with variable coefficients. The effects of gradient variation on the phase velocity and the coupled electromechanical factor are discussed in detail. The analysis shows that the number of vibration modes is greater than that in the non-graded layer structure, and the coupled electromechanical factor increases with the increase of piezoelectric constant graded variation. Presented results are useful for the improvement of properties of surface acoustic wave (SAW) devices.     

An exact analytical solution for freely vibrating piezoelectric coupled circular/annular thick plates using Reddy plate theory

Based on third-order shear deformation plate theory of Reddy, the authors aim to provide an exact analytical solution for free vibration analysis of thick circular/annular plates, both upper and lower surfaces of which are in contact with a piezoelectric layer. Natural frequencies are determined by the solution of the coupled electromechanical governing equations for a combination of free, soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the plate. The electrodes on each piezoelectric layer are assumed to be short-circuited. The Maxwell electrostatics equation is satisfied by adopting a half-sine distribution of the electric potential in the transverse direction of the piezoelectric layers. A comparison of the present exact natural frequencies for piezoelectric coupled circular/annular plates with different boundary conditions is made with previously published results obtained by the Mindlin plate theory and 3-D modified finite element method. The effects of plate parameters such as host thickness to radius ratios, inner to outer radius ratios and piezoelectric to host thickness ratios on the natural frequencies of laminated circular/annular plates are investigated for different combinations of boundary conditions. Results obtained by the present exact closed-form solutions can be served as benchmark data for investigators to validate their numerical and analytical methods in the future.     

Hamilton体系下的功能梯度电磁弹性固体内的导波研究

根据Hamilton原理建立了三维压电压磁动力学耦合系统的Hamilton对偶体系，将经典的弹性力学一类变量问题转化为二类变量，建立了Hamilton正则方程组，研究了功能梯度电磁材料（FGMM）板／管内的弹性导波的频散特性及波结构特征。结果表明：（1）压电效应提高了Lamb波的频率和波速，而磁效应则相反，压电效应对波动的影响远大于磁效应；它们而对SH波没有影响（厚度方向极化）。（2）短路及断路电学边界条件对SH波不发生任何影响（厚度方向极化），而短路对Lamb波的频率和波速有不同程度的降低（相同波数下）。（3）在波结构上，对平板而言，所谓的“对称”和“反对称”Lamb波由于材料的梯度特性而变得不再严格的关于中心线对称或反对称。对管而言，由于材料的非均匀分布导致存轴对称栩转波模态中出现了横截面翘曲现象．轴对称纵向波也出现厚度剪切应力。     

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。     

Effect of Electric Field on the Response of Clamped-FreeMagnetostrictive/Piezoelectric/Magnetostrictive Laminates

This work deals with the response of clamped-free magnetostrictive/piezoelectric/magnetostrictive laminates under electric field both numerically and experimentally. The laminate is fabricated using two magnetostrictive Terfenol-D layers and a soft piezoelectric PZT layer. Easy axis of Terfenol-D layers is length direction, while the polarization of PZT layer is the thickness direction. The magnetostriction of the Terfenol-D layers bonded to the upper and lower surfaces of the PZT layer is first measured. Next, a nonlinear finite element analysis is employed to evaluate the second-order magnetoelastic constants in the Terfenol-D layers bonded to the PZT layer using measured data. The induced magnetic field and internal stresses for the laminates under electric field parallel to the poling are then calculated and discussed in detail. In addition, the induced magnetic field is measured, and test results are presented to validate the predictions.     

Transference of SH waves through irregular interface between corrugated piezoelectric layer and prestressed viscoelastic substrate

An exact approach is used to investigate the horizontally polarized shear wave in an irregular piezoelectric layer with corrugated surface lying over prestressed viscoelastic substrate. Perturbation technique is used to solve the problem. Dispersion relations are obtained in closed form for electrically open and short cases. The main feature of the present work is its ability to investigate the effect of irregularity, corrugation, dielectric constant, piezoelectric constant, initial stress and viscoelastic parameter on the phase velocity of SH wave. Numerical example has been carried out to observe the profound effect of these affecting parameters on phase velocity of SH wave.     

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.     

Shear horizontal wave propagation in periodically layeredcomposites

The transverse resonance approach to guided wave analysis is applied to shear horizontal (SH) wave propagation in periodically layered composites. It is found for SH waves that at high values of the guided wavevector β, the wave energy is trapped in the slower of the two media and propagates accordingly at the slower wavespeed. At low values of β, however, the modes demonstrate a clustering behavior, indicative of the underlying Floquet wave structure. The number of modes in a cluster is observed to correlate with the number of unit cells in the layered plate. New physical insights into the behavior of these systems are obtained by analyzing the partial waves of the guided SH modes in terms of Floquet waves. We show that the fast and slow shear waves in the periodically layered composite play an analogous role to the longitudinal and shear partial waves comprising Lamb waves in a homogeneous plate     

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.     

Optimal design in vibration control of adaptive structures using a simulated annealing algorithm

Advanced reinforced composite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the development of smart structures. These structures offer potential benefits in a wide range of engineering applications such as vibration and noise suppression, shape control and precision positioning. This paper presents a finite element formulation based on the classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as sensors and actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one additional electrical potential degree of freedom for each surface bonded piezoelectric element layer or patch. The control is initialized through a previous optimization of the core of the laminated structure, in order to minimize the vibration amplitude and maximize the first natural frequency. Also the optimization of the patches position is performed to maximize the piezoelectric actuators efficiency. The simulated annealing algorithm is used for these purposes. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers or patches, and to calculate the dynamic response of the laminated structures the Newmark method is considered. The model is applied in the optimization of an illustrative adaptive laminated plate case. The influence of the position and number of piezoelectric patches, as well as the control gain, are investigated and the results are presented and discussed.     

Lamb waves in a thin isotropic layer between two anisotropic layers

Attenuative Lamb wave propagation in adhesively bonded anisotropic composite plates is introduced. The isotropic adhesive exhibits viscous behavior to stimulate the poor curing of the middle layer. Viscosity is assumed to vary linearly with frequency, implying that attenuation per wavelength is constant. Attenuation can be implemented in the analysis through modification of elastic properties of isotropic adhesive. The new properties become complex, but cause no further complications in the analysis. The characteristic equation is the same as that used for the elastic plate case, except that both real and imaginary parts of the wave number (i.e., the attenuation) must be computed. Based on the Lowe's solution in finding the complex roots of characteristic equation, the effect of longitudinal and shear attenuation coefficients of the middle adhesive layer on phase velocity dispersion curves and attenuation dispersion curves of Lamb waves propagating in bonded anisotropic composites is visualized numerically.     

Shape control of smart composite plate with non-rectangular piezoelectric actuators

Quasi-static shape control of a smart structure may be achieved through optimizing the applied electric fields, loci, shapes and sizes of piezoelectric actuators attached to the structure. In this paper, a finite element analysis (FEA) software has been developed for analyzing static deformation of smart composite plate structures with non-rectangular shaped PZT patches as actuators. The mechanical deformation of the smart composite plate is modeled using a 3rd order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation is verified by comparing with experimentally measured deformation. Numerical results are obtained for the optimum values of the electric field in the PZT actuators to achieve the desired shape using the linear least square (LLS) method. The numerical results demonstrate the influence of the shapes of actuators.     

Very small IF resonator filters using reflection of shear horizontal wave at free edges of substrate

A conventional surface acoustic wave (SAW) resonator filter requires reflectors consisting of numerous grating fingers on both sides of interdigital transducers (IDTs). On the contrary, it is considered that small-sized and low loss resonator filters without reflectors consisting of grating fingers can be realized by exploiting this characteristic of the shear horizontal (SH) wave or the Bleustein-Gulyaev-Shimizu (BGS) wave. There are two types of resonator filters: transversely coupled and longitudinally coupled. No transversely coupled filters (neither conventional nor edge-reflection) using the SH wave on a single-crystal substrate have been realized until now, because two transverse modes (symmetrical and asymmetrical modes) are not easily coupled. However, the authors have realized small low loss transversely coupled resonator filters in the range of 25 to 52 MHz using edge reflections of the BGS wave on piezoelectric ceramic (PZT: Pb(Zr,Ti)O/sub 3/) substrates for the first time by developing methods by which the two transverse modes could be coupled. Also the authors have realized small low loss longitudinally coupled resonator filters in the range of 40 to 190 MHz using edge reflection of BGS or SH waves on PZT or 36/spl deg/-rotated-Y X-propagation LiTaO/sub 3/ substrates for the first time. Despite being IF filters, their package (3/spl times/3/spl times/1.03 mm/sup 3/) sizes are as small as those of RF SAW filters.