Wave propagation in non-homogeneous magneto-electro-elastic hollow cylinders

A dynamic solution is presented for the propagation of harmonic waves in imhomogeneous (functionally graded) magneto-electro-elastic hollow cylinders composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The Legendre orthogonal polynomial series expansion approach is employed to determine the wave propagating characteristics in the hollow cylinders. The dispersion curves of the imhomogeneous piezoelectric-piezomagnetic hollow cylinder and the corresponding non-piezoelectric and non-piezomagnetic hollow cylinders are calculated to show the influence of the piezoelectricity and piezomagnetism. Electric potential and magnetic potential distributions are obtained to illustrate the different influences of the piezoelectricity and piezomagnetism and the different influences of the piezoelectric effect and piezomagnetic effect on longitudinal modes and torsional modes. For the radial polarizing piezoelectric-piezomagnetic hollow cylinder, the piezoelectric effect and piezomagnetic effect take mostly on the longitudinal mode. Finally, a hollow cylinder at different ratio of radius to thickness is calculated to show the influence of the ratio on the piezoelectric effect and piezomagnetic effect.     

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.     

SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface

In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe₂O₄ composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices.     

FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES

Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions. For any homogeneous layer, we construct the general solution in terms of a simple formalism that resembles the Stroh formalism, from which any physical quantities can be solved for given boundary conditions. In particular, the dispersion equation that characterizes the relationship between the natural frequency and wavenumber can be obtained in a simple form. For multilayered plates, we derive the dispersion relation in terms of the propagator matrices. The present solution includes all previous solutions, such as piezoelectric, piezomagnetic, and purely elastic solutions as special cases, and can serve as benchmarks to various thick plate theories and numerical methods used for the modelling of layered composite structures. Typical natural frequencies and mode shapes are presented for sandwich piezoelectric/piezomagnetic plates. It is shown clearly that some of the modes are purely elastic while others are fully coupled with piezoelectric/piezomagnetic quantities, with the latter depending strongly upon the material property and stacking sequence. These frequency and mode shape features could be of particular interest to the analysis and design of various “smart” sensors/actuators constructed from magneto-electro-elastic composite laminates.     

Hybridization of acoustic waves in piezoelectric plates

The interaction (hybridization) of different types of acoustic waves of zero and higher orders propagating in lithium niobate piezoelectric plates is theoretically investigated. Different crystallographic orientations of the plates and different directions of wave propagation in them are considered. It is shown that, for an electrically free plate with the propagation direction along any of the crystallographic axes, the dispersion curves have intersection points and hybridization is absent. However, when the propagation direction slightly changes or when one of the plate surfaces is short-circuited, the dispersion curves separate and the waves become coupled. A quantitative coefficient characterizing the degree of wave hybridization with allowance for both mechanical and electric coupling is introduced. It is shown that the dependence of this coefficient on the product of the plate thickness by the wave frequency determines the extent of separation of the dispersion curves of interacting waves. The phenomenon under study is of both fundamental and practical interest, for example, in connection with the problem of an efficient excitation of nonpiezoactive acoustic waves in piezoelectric plates.     

Dynamic stress from a circular hole in a functionally graded piezoelectric/piezomagnetic material subjected to shear waves

An analytical method is applied to investigate the scattering of magneto-electro-elastic waves and dynamic stress around a circular hole in a functionally graded piezoelectric/piezomagnetic material layer. Analytical solutions of the wave, electric and magnetic fields are expressed by employing a wave function expansion method. Analyses show that the piezoelectric and piezomagnetic properties greatly affect the dynamic stress in the region of the intermediate frequency, and the effect increases with increasing non-homogeneous parameter. The effects of the incident wave number and non-homogeneous parameter of the materials on the dynamic stress and electric field are also examined.     

SH wave propagation in magnetic–electric periodically layered plates

In this paper, dispersive behavior and band structure of SH waves in magnetic–electric (ME) periodically layered plate are investigated by the transfer matrix method. Two kinds of unit cell form, one is piezoelectric (PE)/piezomagnetic (PM)/PE, and the other is PM/PE/PM, are considered in detailed. A peculiar case of the generalized single-celled plate is first presented and then the multi-celled periodical layered plates for discussion on the propagation behaviors and the band characteristics of SH waves, respectively. The effects on dispersive curves of four kinds of ME boundary conditions at the free surface of plates are discussed. Numerical examples for phase velocities or frequencies all show that the zero-order mode is non-dispersive both for single-celled and multi-celled periodically layered plates. The high modes of dispersive curves tend to the shear wave velocity of the slower sub-layer as frequencies increase both for these two structures. The frequency pass-band and frequency band gaps appear in multi-layered ME periodically layered plates. Electrical and magnetic boundary conditions, respectively, determine the dispersive curves for SH waves in the PE/PM/PE and PM/PE/PM periodically layered plates.     

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

Wave propagation in a magneto-electroelastic plate

The wave propagation in a magneto-electro-elastic plate was studied. Some new characteristics were discovered: the guided waves are classified in the forms of the Quasi-P, Quasi-SV and Quasi-SH waves and arranged by the standing wavenumber; there are many patterns for the physical property of the magneto-electro-elastic dielectric medium influencing the stress wave propagation. We proposed a self-adjoint method, by which the guided-wave restriction condition was derived. After the corresponding orthogonal sets were found, the analytic dispersion equation was obtained. In the end, an example was presented. The dispersive spectrum, the group velocity curved face and the steady-state response curve of a magneto-electro-elastic plate were plotted. Then the wave propagations affected by the induced electric and magnetic fields were analyzed. Supported by the National Natural Science Foundation of China (Grant Nos. 10572001 and 10232040)     

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.     

压电网络复合板的波动特性与隔声性能分析

在压电网络复合板机电耦合波动方程基础上,首先对在其中传播的弯曲波的波动特性进行了分析,发现压电网络复合板中同时存在两种不同频散特性的弯曲波,电感电阻并联型压电网络复合板中存在的两种弯曲波的频散曲线具有频率转向现象;在频率转向区,弯曲波的衰减常数或达到最大或迅速增大这一结论为压电网络复合板的减振降噪设计提供了参考。对压电网络复合板中的能量分析给出了这一结论的机理:即在频率转向区板中的机械能与电能能够进行最大的能量交换;在波动分析的基础上对压电网络复合板的隔声特性进行了分析,发现压电网络复合板隔声曲线上的低谷随外界电感值的变化能够发生移动或者消失,最后结合压电网络复合板的波动频散特性对复合板的隔声机理进行了分析,为设计压电网络复合板的隔声性能提供了理论参考。     

Resonance frequencies of piezoelectric plates surrounded by solid and fluid half-spaces

The design of ultrasound transducers, resonators and other piezoelectric devices usually requires the calculation of the resonance frequencies of piezoelectric plates. Recent studies have shown that the resonance frequencies for plates in vacuum correspond to frequencies where the waveguide group velocity vanishes (zero-group-velocity points). However, those studies are limited to vacuum boundary conditions. The objective of the present study is to analyze the resonance frequencies of layered piezoelectric plates in contact with solid and fluid half-spaces and their relation to the dispersion behavior of the elastic guided wave propagation. Theoretical analysis using partial-wave approach of leaky Lamb waves is performed to study wave propagation in, and resonance behavior of, multilayered plates in contact with solid and fluid half-spaces. A novel observation resulted from this analysis is that, for plates in contact with solid and fluid half-spaces, the resonance frequencies occur at points where the magnitude of the wavenumber reaches a minimum. This frequency is named as a ‘transition frequency’. Such observations are important because they allow an easy identification of resonance frequencies with high amplitude response directly from the dispersion curves. This study will be helpful for the design of piezoelectric components used for resonators and sensors.     

Consideration of SH-wave fundamental modes in piezoelectromagnetic plate: electrically open and magnetically open boundary conditions

This report studies the dispersive wave propagation in the transversely isotropic (6?mm) piezoelectromagnetic (PEM) plate when the mechanical, electrical, and magnetic boundary conditions for both the upper and lower free surfaces of the plate are as follows: the mechanically free, electrically open, and magnetically open surfaces. This study follows some original results obtained in book. The fundamental modes’ dispersion relations are graphically shown for the following well-known PEM composite materials: BaTiO₃–CoFe₂O₄ and PZT-5H–Terfenol-D. It is natural that for large values of the nondimensional parameter kd (k is the wave number and d is the plate half-thickness), the velocities of both the fundamental modes approach the surface shear-horizontal wave called the piezomagnetic exchange surface Melkumyan wave. It is well known that plate waves are usually utilized in the nondestructive testing and evaluation, for instance, in the airspace industry. Also, PEM materials are used as smart ones in various technical devices such as dispersive wave delay lines, (biochemi)sensors, lab-on-a-chip, etc.     

Propagation of SH waves in layered functionally gradient piezoelectric–piezomagnetic structures

Abstract

The propagation of SH waves is studied in two bonded semi-infinite material, one piezoelectric and the other piezomagnetic. Both materials are functionally gradient materials. The material properties of the two materials vary in two directions, one parallel to the interface and the other perpendicular to the interface. The dispersion relations are obtained in explicit forms for different forms of the non-homogeneities. The effects of gradient variation about material constants on the frequency of SH waves and on the wave numbers are shown graphically.     

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.     

Free vibration behaviour of multiphase and layered magneto-electro-elastic beam

Free vibration studies of multiphase and layered magneto-electro-elastic beam for BaTiO₃–CoFe₂O₄ composite is carried out. In-plane plate finite-element analysis is used to obtain the behaviour of magneto-electro-elastic beam. Studies are carried out for beams for different boundary conditions, as may be applicable in design of smart sensors/actuators. The ANSYS package is used to validate the results obtained by the computer code developed for piezoelectric (PE) beam. Plane stress condition is used for the Euler–Bernouli magneto-electro-elastic beam.     

Reverberation-ray matrix analysis for wave propagation in multiferroic plates with imperfect interfacial bonding

The dispersion behavior of waves in multiferroic plates with imperfect interfacial bonding has been investigated via the method of reverberation-ray matrix, which is directly established from the three-dimensional equations of magneto-electro-elasticity in the form of state space formalism. A generalized spring-layer model is employed to characterize the interfacial imperfection. By introducing a dual system of local coordinates for each single layer, the numerical instability usually encountered in the state space method can be avoided. Based on the proposed method, a typical sandwich plate made of piezoelectric and piezomagnetic phases is considered in numerical examples to calculate the dispersion curves and mode shapes. It is demonstrated that the results obtained by the present method is unconditionally stable as compared to the traditional state space method. The influence of different interfacial bonding conditions on the dispersion characteristics and corresponding mode shapes is investigated.     

Anomalous dispersion of SH acoustic waves in a piezoelectric sandwich structure

A transformation of the dispersion spectrum of shear horizontal (SH) acoustic eigenwaves in a sandwich structure due to a piezoelectric effect is described. The structure consists of two plates separated by a gap whose thickness is considerably less than the wavelength. Under these conditions, acoustic fields induced in the plates interact through the piezoelectric effect. The piezoelectric effect brings about a distortion and divergence of the initially (in the zeroth approximation) independent dispersion curves; i.e., all points of intersection of the dispersion curves disappear. Each of the new dispersion branches is formed by a set of adjacent portions of initial branches. A change in the wave number (or in the frequency) results in a periodic gradual displacement of the localization zone of the acoustic field from one plate to the other.     

Thickness-shear vibration of a quartz plate connected to piezoelectric plates and electric field sensing

We study thickness-shear vibration of a quartz plate connected to two piezoelectric ceramic plates with initial deformations caused by a biasing electric field. The theory for small deformations superposed on finite biasing deformations in an electroelastic body is used. It is shown that the resonant frequencies of the incremental thickness-shear vibration of the quartz plate vary with the biasing electric field. The biasing electric field induced frequency shift depends linearly on the field. Therefore this effect may be used for electric field sensing. The dependence of the electric field induced frequency shift on various material and geometric parameters is examined. When the electric field is of the order of 100 V/mm, the relative frequency shift is of the order of 10⁻⁵. The case when the piezoelectric plates are replaced by piezomagnetic plates is also investigated for magnetic field sensing, and similar results are obtained.     

Wave propagation in layered piezoelectric rectangular bar: An extended orthogonal polynomial approach

Wave propagation in multilayered piezoelectric structures has received much attention in past forty years. But the research objects of previous research works are only for semi-infinite structures and one-dimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes an extension of the orthogonal polynomial series approach to solve the wave propagation problem in a two-dimensional (2-D) piezoelectric structure, namely, a multilayered piezoelectric bar with a rectangular cross-section. Through numerical comparison with the available reference results for a purely elastic multilayered rectangular bar, the validity of the extended polynomial series approach is illustrated. The dispersion curves and electric potential distributions of various multilayered piezoelectric rectangular bars are calculated to reveal their wave propagation characteristics.