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.     

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.     

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.     

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.     

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.     

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.     

三层介质超声谐振模式随材料和界面粘接性能变化的演变规律

在用超声波谐振对粘接材料的粘接强度进行无损评估时, 不同模式对粘接强度的敏感程度受到众多因素和参数的影响, 对检测结果的可靠性至关重要. 基于多层介质中声传播和界面弱粘接边界条件的理论模型, 将一个上下非对称的金属-粘接剂-金属三层结构的平面波反射系数函数中的谐振模式看作是上下铝金属层各自的Lamb波频散模式通过夹心粘接剂层相互耦合后叠加组成. 改变影响结构粘接强度的因素, 即粘接剂的性能参数(声阻抗、密度、厚度)和界面切向劲度系数k_t来分析三层结构谐振模式耦合方式的变化,得出结论: 粘接结构粘接性能的变化基本上不改变与被粘铝层相关的固有部分的Lamb波模式, 而它们的耦合模式则在谐振频率上产生平移并会与固有模式进行交换和替代; 不同参数的变化引起的模式演变有各自的规律, 大多可彼此区分.     

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.     

钢-混凝土结构弱粘接界面缺陷的超声导波检测*

钢-混凝土结构是土木工程中的一种常用结构形式,钢与混凝土粘接处可能出现弱粘接甚至完全脱粘的缺陷,严重影响结构的安全性。该文提出利用空气耦合超声导波衰减的方法实现钢-混凝土结构粘接状态的非接触无损检测方法,分析不同厚度粘接界面对超声导波衰减的影响。基于全局矩阵技术对钢-混凝土结构求解理论频散方程和衰减曲线,得到界面层不同粘接条件下的理论参数及衰减特性。建立不同粘接条件的有限元模型,定量分析不同模态对粘接缺陷的检测敏感度。研究界面层厚度分别为1 mm和2 mm两种情况下S0能量的衰减情况。研究结果表明:S0模态可有效判断粘接结构的粘接状态,对于同一界面层厚度,随着界面粘接条件变弱,S0最大幅值与A0最大幅值比不断增大;不同厚度同一粘接条件下,2 mm相较于1 mm该值更大。该方法在钢-混凝土结构粘接界面缺陷的检测方面具有良好的应用价值和发展前景。     

Excitation of surface elasticity waves in piezoelectric media by ion beams∗

Kinetically it has been shown that by considering a semi-bounded piezoelectric medium with hexagonal symmetry with an ion beam flowing on its free surface, the surface elasticity waves can be excited on their surface-vacuum interface as a result of the piezoelectric effect.     

Low-frequency magnetic energy harvest using multiferroic composite plates

It is shown with a theoretical bending model that a laminated plate with piezoelectric and piezomagnetic layers can be used to harvest magnetic energy at relatively low frequencies. The output electric power and the energy conversion efficiency are calculated. The load dependence of the magnetoelectric coupling coefficient is obtained.     

Magneto-electric coupling in piezoelectric-piezomagnetic superlattices

A piezoelectric-piezomagnetic superlattice (PPS) is proposed to present the magneto-electric (ME) coupling wherein electric polarization induces magnetization or vice versa through the layer's coherent strain. We reveal that in PPS, the interaction of electromagnetic waves with the correspondent alternative piezoelectric and piezomagnetic superlattices through their vibrations excites the piezoelectric and the piezomagnetic phonon polaritons simultaneously. The polaritons couple with each other to give rise to a stop band, in which double negative permittivity and permeability can be realized, however negative refraction could not occur. The coupling also results in the huge dynamic ME effect which attributes to the large ME voltage coefficient in a BaTiO₃-CoFe₂O₄ superlattice as large as 14.9 V cm⁻¹ Oe⁻¹.     

Wave propagation in non-homogeneous magneto-electro-elastic plates

A dynamic solution is presented for the propagation of harmonic waves in imhomogeneous (functionally graded) magneto-electro-elastic plates 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 plates. The dispersion curves of the imhomogeneous piezoelectric–piezomagnetic plate and the corresponding non-piezoelectric, non-piezomagnetic plates are calculated to show the influences of the piezoelectricity and piezomagnetism on the dispersion curves. They are compared with the dispersion curves of the plates with the different magnetic constants to illustrate the influential factors of the piezoelectric and piezomagnetic effect for the wave propagation in a magneto-electro-elastic plate. Electric potential and magnetic potential distributions at different wavenumbers are also obtained to illustrate the different influences of the piezoelectricity and piezomagnetism.     

Reflection and transmission of waves in pyroelectric and piezoelectric materials

The reflection and transmission theories of waves in pyroelectric and piezoelectric medium are studied in this paper. In general in an infinite homogeneous pyroelectric medium there are four bulk wave modes: quasi-longitudinal, two quasi-transversal and temperature waves. In an infinite homogeneous piezoelectric medium there are three bulk wave modes: quasi-longitudinal and two quasi-transversal waves. In the reflection and transmission problem there are five complex boundary conditions in the pyroelectric medium and four complex boundary conditions for the piezoelectric medium. In this paper, we find that the surface waves will be revealed in the reflection and transmission wave problem. The surface waves have the same wave vector component with the incident waves on the interface plane. The two dimensional reflection problem of waves at the interface between the semi-infinite pyroelectric medium and vacuum is researched in greater detail and a numerical example is given.     

Effective properties of coated fibrous piezoelectric composites with spring-type interfaces under anti-plane mechanical and in-plane electrical loads

In this paper, we investigate the effective properties of three-phase(matrix/coating/fiber) cylindrical piezoelectric composites with imperfect interfaces under anti-plane mechanical and in-plane electrical loads. By using the electromechanically coupling spring-type interface model and the generalized self-consistent method(GSM), we analytically derived the effective electroelastic moduli. The present solutions include as special cases the three-phase cylindrical piezoelectric composites with perfect interfaces as well as the two-phase(matrix/fiber) case with imperfect or perfect interfaces. Selected calculations are graphically shown to demonstrate dependence of the effective moduli on the interfacial properties. The particular size-dependent characteristic due to the interfacial imperfection is also discussed.     

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.     

Shear waves guided by the imperfect interface of two magnetoelectric materials

In this paper, propagation of shear waves along a weak interface of two dissimilar magnetoelectric or magnetoelectroelastic materials is considered. Two exact dispersion relations are obtained for an imperfect electrode interface and an unelectroded interface, respectively. The existence condition of the interfacial waves is studied. Our results show that the interfacial imperfection strongly affects the velocity of the interfacial shear waves. In particular, for certain bi-magnetoelectric material, the interfacial shear waves may do not exist for a perfect interface and exist only for an imperfect interface. These findings are useful for the design of high-frequency wave devices.     

Effect of an imperfect interface on the SH wave propagating in a cylindrical piezoelectric sensor

Under harsh in situ conditions, the interface in piezoelectric sensors may be damaged mechanically and/or electrically. The damaged interface would in turn affect the electromechanical behaviors of the sensors. The purpose of the present work is to study the effect of the imperfect interface on SH wave propagating in a cylindrical piezoelectric sensor. The dispersion relations of SH wave are derived analytically and the phase velocity are obtained numerically. Parametric studies on the phase velocity indicate that the mechanical imperfection may reduce the phase velocity under certain circumstances; however, the electrical imperfection has no obvious effect on the phase velocity in any cases; with the thickness of the piezoelectric layer increasing, the phase velocity may increase, decrease or keep unchanged, depending on the combination of the values of the wave number and the mechanical imperfection parameter.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)     

Propagation behaviors of thickness-twist modes in an inhomogeneous piezoelectric plate with two imperfectly bonded interfaces

The thickness-twist modes in an inhomogeneous piezoelectric plate with two imperfectly bonded interfaces are analyzed, and an exact solution is obtained according to the spring-type relation from the equations of the linear theory of piezoelectricity. The frequency shift, the displacement and the stress components are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of mechanical imperfection is more evident than that of the electrical imperfection on the thickness-twist modes. Results show that the displacement and the stress components all change obviously due to the imperfectly bonded interfaces. The relationship between the frequency shift Δω and the non-dimensional number γ that is related to the imperfect interfaces is linear, which can be used to provide the foundation for a new experimental procedure for measuring the level of the interface bonding.