非理想界面弹性层/压电柱结构中SH波的传播特性

研究了各向同性弹性层与压电柱之间非理想连接时沿周向传播的SH波的频散特性.弹性层表面力学自由;弹性层与压电柱之间应力连续、位移间断.通过求解控制方程,将问题的解用Bessel函数表示,利用界面条件和边界条件得到频散方程,然后对其进行数值求解,分析了界面性态、材料常数和几何尺寸对SH波传播特性的影响.     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.     

Analysis of wave propagation in piezoelectric coupled cylinder affected by transverse shear and rotary inertia

In this paper, we examine the wave propagation in a piezoelectric coupled cylindrical shell affected by the shear effect and rotary inertia. A complete mathematical analysis of wave propagation solution in this piezoelectric coupled cylindrical shell is provided. The dispersion characteristics are derived through the solving an eigenvalue problem. Results are validated by the classical solution of a metallic cylinder. Besides providing and discussing the dispersion curves for different wave modes, we also examine the piezoelectric effects on the dispersion curves. Further to the above investigation, comparison of dispersion solutions from different shell theories is also conducted. This work may serve as a benchmark for wave propagation in piezoelectric coupled cylindrical shells.     

Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer

This paper presents the wave propagation in a cylinder coated with a thin piezoelectric layer. The piezoelectric coupling effects are fully modeled in the mechanics model for this piezoelectric coupled cylindrical shell with bending resistance. The decoupled torsional wave velocity and the dispersion curves for the two- mode shell model are obtained theoretically. The cut-off frequency and phase velocities at limit wave number are also derived. The numerical simulations are conducted to present the results of wave propagation in this cylindrical shell and as well as to compare the results by the current bending theory and the membrane shell theory. From the comparisons, the results display obvious deference of wave propagations in terms of dispersion characteristics by different shell theories when thicker piezoelectric layer are used and when higher wave number is considered. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.     

3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid

The free vibration of an arbitrarily thick orthotropic piezoelectric hollow cylinder with a functionally graded property along the thickness direction and filled with a non-viscous compressible fluid medium is investigated. The analysis is directly based on the three-dimensional exact equations of piezoelasticity using the so-called state space formulations. The original functionally graded shell is approximated by a laminate model, of which the solution will gradually approach the exact one when the number of layers increases. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement at the interface. Analytical frequency equations are derived for different electrical boundary conditions at two cylindrical surfaces. As particular cases, free vibration of multi-layered piezoelectric hollow cylinder and wave propagation in infinite homogeneous cylinder are studied. Numerical comparison with available results is made and dispersion curves predicted from the present three-dimensional analysis are given. Numerical examples are further performed to investigate the effects of various parameters on the natural frequencies.     

Anti-plane waves near an interface between two piezoelectric half-spaces

We show the existence of certain new waves that can propagate near an interface between two half-spaces of different piezoelectric ceramics, where the interface is modeled by a membrane with the surface/interface elasticity [1]. The current configuration can be reduced into a number of well-known results as special cases, such as Love wave, Bleustein and Gulyaev wave. Together with our previous work for the imperfect interface [2], a full range of consideration of the interface affecting the anti-plane waves is now completed.     

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.     

多层电磁弹性圆柱壳内波的轴向传播

对多层电磁弹性圆柱壳内波的轴向传播进行了分析。根据柱坐标系下电磁弹性多层结构的几何方程、平衡方程和本构方程,推导出了两个层间变量所满足的状态方程。通过状态方程的解和层间变量连续性条件,得到了多层圆柱体内外表面层间变量的传递关系。最后利用边界条件,导出了波在传播时所满足的频散方程,并求得该结构的模态参数。以一个三层的压电/压磁材料组成的柱壳结构作为数值算例,计算出波在其中轴向传播时的频散关系和模态参数,并对计算结果进行了分析。     

Electroelastic interaction between piezoelectric screw dislocation and circularly layered inclusion with imperfect interfaces

The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids is theoretically investigated.Here,the dislocation located at arbitrary points inside either the matrix or the inclusion and the interfaces of the interphase layer are imperfect.By the complex variable method,the explicit solutions to the complex potentials are given,and the electroelastic fields can be derived from them.The image force acting on the dislocation can be obtained by the generalized PeachKoehler formula.The motion of the piezoelectric screw dislocation and its equilibrium positions are discussed for variable parameters.The important results show that,if the inner interface of the interphase layer is imperfect and the magnitude of degree of the interface imperfection reaches the certain value,two equilibrium positions of the piezoelectric screw dislocation in the matrix near the interface are found for the certain material combination which has never been observed in the previous studies(without considering the interface imperfection).     

Anti-symmetric waves in pre-stressed imperfectly bonded incompressible elastic layered composites

The effect of an imperfect interface on the dispersive behavior of in-plane time-harmonic symmetric waves in a pre-stressed incompressible symmetric layered composite, was analyzed recently by Leungvichcharoen and Wijeyewickrema (2003). In the present paper the corresponding case for time harmonic anti-symmetric waves is considered. The bi-material composite consists of incompressible isotropic elastic materials. The imperfect interface is simulated by a shear-spring type resistance model, which can also accommodate the extreme cases of perfectly bonded and fully slipping interfaces. The dispersion relation is obtained by formulating the incremental boundary-value problem and using the propagator matrix technique. The dispersion relations for anti-symmetric and symmetric waves differ from each other only through the elements of the propagator matrix associated with the inner layer. The behavior of the dispersion curves for anti-symmetric waves is for the most part similar to that of symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress for perfectly bonded and imperfect interface cases, a finite phase speed may exist only for the fundamental mode while other higher modes have an infinite phase speed. However, for a fully slipping interface in the low wavenumber region it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the phase speeds of the surface wave or the interfacial wave or the limiting phase speed of the composite. The bifurcation equation obtained from the dispersion relation yields neutral curves that separate the stable and unstable regions associated with the fundamental mode or the next lowest mode. Numerical examples of dispersion curves are presented, where when the material has to be prescribed either Mooney–Rivlin material or Varga material is assumed. The effect of imperfect interfaces on anti-symmetric waves is clearly evident in the numerical results.     

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.     

Dispersion effects of extensional waves in pre-stressed imperfectly bonded incompressible elastic layered composites

The effect of an imperfect interface, on time-harmonic extensional wave propagation in a pre-stressed symmetric layered composite is considered. The bimaterial composite consists of incompressible isotropic elastic materials. The shear spring type resistance model employed to simulate the imperfect interface can accommodate the extreme cases of perfect bonding and a fully slipping interface. The dispersion relation obtained by formulating the incremental boundary-value problem and the use of the propagator matrix technique, is analyzed at the low and high wavenumber limits. For the perfectly bonded and imperfect interface cases in the low wavenumber region, only the fundamental mode has a finite phase speed, while other higher modes have an infinite phase speed when the dimensionless wavenumber approaches zero. However, for the fully slipping interface in the low wavenumber region, both the fundamental mode and the next lowest mode have finite phase speeds. In the high wavenumber region, when the dimensionless wavenumber tends to infinity, the phase speeds of the fundamental mode and the higher modes depend on the phase speeds of the surface and interfacial waves and on the limiting phase speed of the composite. An expression to determine the cut-off frequencies is obtained from the dispersion relation. Numerical examples of dispersion curves are presented, where when the material has to be prescribed either Mooney–Rivlin material or Varga material is assumed. The effect of the imperfect interface is clearly evident in the numerical results.     

Wave characteristics in functionally graded piezoelectric hollow cylinders

Based on linear three-dimensional piezoelasticity, the Legendre orthogonal polynomial series expansion approach is used for determining the wave characteristics in hollow cylinders composed of the functionally graded piezoelectric materials (FGPM) with open circuit. The displacement and electric potential components, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Dispersion curves for FGPM and the corresponding non-piezoelectric hollow cylinders are calculated to show the piezoelectric effect. The influence of the ratio of radius to thickness is discussed. Electric potential and displacement distributions are used to show the piezoelectric effect on the flexural torsional mode. The influence of the polarizing direction on the piezoelectric effect is illustrated. For the radial and axial polarization, the piezoelectric effect reacts mostly on the longitudinal mode. For circumferential polarization, the piezoelectric effect reacts mostly on the torsional mode. In the FGPM hollow cylinder, piezoelectricity can weaken the guided wave dispersion.     

Wave propagation modeling in cylindrical human long wet bones with cavity

The wave propagation modeling in cylindrical human long wet bones with cavity is studied. The dynamic behavior of a wet long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated. An analytical solutions for the mechanical wave propagation during a long wet bones have been obtained for the flexural vibrations. The average stresses of solid part and fluid part have been obtained. The frequency equations for poroelastic bones are obtained when the medium is subjected to certain boundary conditions. The dimensionless frequencies are calculated for poroelastic wet bones for various values for non-dimensional wave lengths. The dispersion curves of the dry bone and wet bone for the flexural mode n=2 are plotted. The numerical results obtained have been illustrated graphically.     

Dynamic effective property of fibrous piezoelectric composites with spring- or membrane-type imperfect interfaces

The present paper studies the dynamic effective property of piezoelectric composites embedded with cylindrical piezoelectric fibers under anti-plane harmonic electro-elastic waves. By using the dynamic generalized self-consistent method (DGSM) of electro-elastic coupling wave, the problem of randomly distributed cylindrical fibers in a piezoelectric medium can be analyzed in terms of a representative volume element with a coated fiber embedded in an equivalent effective medium. The interfaces between the fibers and the matrix are assumed to be imperfect which are here modeled as spring- or membrane-type interfaces. Through wave function expansion method and an iterative method, the effective piezoelectrically stiffened shear modulus and the effective wave number are obtained. Examples are conducted to verify the present solutions and to illustrate the dependence of the effective piezoelectrically stiffened shear modulus on the wave number (frequency) as well as the interface properties. The special size effect related to interfacial imperfection is also discussed.     

Theoretical transient analysis and wave propagation of piezoelectric bi-materials

The transient response of piezoelectric bi-materials subjected to a dynamic anti-plane concentrated force or electric charge with perfectly bonded interface is examined in the present study. The problem is solved by using the Laplace transform method and the inverse Laplace transform is evaluated by means of Cagniard’s method. Exact transient full-field solutions of the contribution for each wave are expressed in explicit closed forms. The transient behavior of field quantities is examined in detail by numerical calculations. The existence condition of a propagating surface wave along the interface is discussed in detail. A surface wave can be guided by the interface of two semi-infinite materials in contact if one, at least, of these two materials is piezoelectric. The propagation velocity of the surface wave is explicitly expressed and is found to be less than the lower shear wave velocity of the two materials. The existence of the surface wave for piezoelectric–piezoelectric bi-materials is restricted to the situation that the shear waves of the two piezoelectric materials are very close. The possibility for the existence of the surface wave for piezoelectric–elastic bi-materials is much greater than that of the piezoelectric–piezoelectric bi-materials.     

含非完整界面的功能梯度压电材料Ⅲ型裂纹问题

本文研究了含非完整界面的功能梯度压电复合材料的Ⅲ型裂纹问题．此裂纹垂直于非完整界面,采用弹簧型力电耦合界面模型模拟非完整界面．界面两侧材料的性质,如弹性模量、压电常数和介电常数均假定呈指数函数形式且沿着裂纹方向变化．运用积分变换法将裂纹面条件转换为奇异积分方程,并使用Gauss-Chebyshev方法对其进行数值求解．根据算例结果讨论了一些退化问题并分析了裂纹尖端强度因子与材料的非均匀系数和非完整界面参数的关系．     

PROPAGATION BEHAVIORS OF SHEAR HORIZONTAL WAVES IN PIEZOELECTRIC-PIEZOMAGNETIC PERIODICALLY LAYERED STRUCTURES

This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.     

Electromechanical Fields Near a Circular PN Junction Between Two Piezoelectric Semiconductors

We study electromechanical fields near the interface between a circular piezoelectric semiconductor cylinder and another piezoelectric semiconductor in which it is embedded.The cylinder is p-doped. The surrounding material is n-doped. The phenomenological theory of piezoelectric semiconductors consisting of the equations of piezoelectricity and the conservation of charge for holes and electrons is used. The theory is linearized for small carrier concentration perturbations. An analytical solution is obtained, showing the formation of a PN junction near the interface. Various electromechanical fields associated with the junction are calculated. The effects of a few physical parameters are examined.     

Influence of imperfect bonding on the reflection and transmission of QP-wave at the interface of two functionally graded piezoelectric materials

This paper studies the reflection and transmission of two dimensional quasi P wave incident at an imperfect interface between two dissimilar Functionally Graded Piezoelectric Materials (FGPM) half-spaces. The imperfect bonding behavior between the two considered half-spaces is described by the interfacial imperfections. The imperfection is characterized by the normal stiffness and tangential stiffness using the linear spring model. These interface parameters (i.e normal stiffness and tangential stiffness) are dependent on the elastic properties of interphase. Secular equations have been derived analytically for both the half-spaces. Different cases of imperfect interfaces namely perfect interface, slip interface, weak bonding interface and unbounded interface have been assumed and discussed. Influence of material gradients on the reflection and transmission coefficients (RTC’s) have been inflicted graphically for all the four considered interface conditions. Further, a comparative study of the RTC’s with respect to the incident angle has been carried out for the different cases of imperfections. The obtained results may be useful for measuring imperfection at the interface and designing of SAW devices.