功能梯度压电夹层结构中SH波的传播

研究了功能梯度压电上、下半空间和均匀压电层组成的夹层结构中SH波的传播性能，上、下功能梯度半空间的材料性能沿垂直于界面方向以指数函数形式变化。首先推导了SH传播时电弹场的解析解，然后利用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，通过数值算例表明了材料性能梯度变化、压电层厚度和材料组合方式对相速度的影响，结果对功能梯度压电材料在声波器件中的应用有参考价值。     

梯度半空间梯度覆层中的Love波

对功能梯度弹性半空间上覆盖一层功能梯度材料中的Love波的频散问题进行了研究，给出 了Love波频散方程的一般形式. 对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运 动控制方程进行了求解，给出了半空间和覆盖层的位移、应力解析解，给出了Love波在该解析 解下的频散方程. 以覆盖层的剪切弹性模量和质量密度均呈指数函数变化，半空间的剪切弹 性模量和质量密度均呈抛物线变化为例，利用迭代方法对频散方程进行了求解，给出了频散 曲线. 结果显示：在最低阶振型频散曲线中出现截止频率.     

广义Rayleigh波的频谱特性分析

本文导出了在加层半空间中广义Ｒａｙｌｅｉｇｈ波的谱函数方程，研究了不同的材料组合对其频率特性的影响，并给出了广义Ｒａｙｌｅｉｇｈ波的相速度随频率变化的计算曲线。     

GAS WAVE IN FUNCTIONALLY GRADED MAGNETO-ELECTRO-ELASTIC COUPLED STRUCTURE

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.     

功能梯度磁电弹耦合结构中的间隙波

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.     

各向异性弹性体光滑接触界面上的滑移脉冲波

利用Stroh公式,Fourier分析和奇异积分方程技术研究了两各向异性弹性半空间光滑接触可分离界面上滑移脉冲波的存在及其传播特性。结果表明,如果至少能在一种介质中存在Rayleigh波,且其波速小于两种介质中的最小极限速度,则滑移脉冲波就可以存在。这种脉冲波传播速度不确定,可在最小极限波速与较低的Rayleigh波速之间取值,而该取值范围又取决于无界面分离情况下的第一、第二滑移波的解。分离区大小取决于扰动的强度,界面法向力和质点速度在分离区两端有 1 /2奇异性。     

含梯度渐变残余应力的弹性半无限体的广义Rayleigh波

研究含梯度残余应力的弹性半无限体的平面应变型表面波,即广义Rayleigh波。将该结构等效为含梯度初应力的弹性覆盖层和无初应力的弹性基底构成的半无限体结构。求得覆盖层中位移函数的幂级数解与均质基底位移函数的解析解,并代入边界条件,得到频散方程。针对拉、压残余应力,分别讨论了其随厚度方向均匀分布、线性变化和指数变化情况下广义Rayleigh波的一阶模态频散特性。数值结果表明:随着拉应力增大,广义Rayleigh波波速会增加,反之,压应力的增大会导致波速的降低;残余应力均匀分布时波速的改变量较大,线性变化次之;当残余应力按照指数函数变化时,梯度参数越趋近于零,其结果越趋近于线性变化情况,随着梯度参数的减小,波速改变量也随之减小。当使用广义Rayleigh波频散特性实现残余应力无损检测时,如果采用与实际梯度渐变残余应力不符的均匀残余应力模型将会低估表面残余应力。本文所得结论可为利用广义Rayleigh波实现梯度残余应力无损检测提供理论基础。     

覆盖层与基底极化方向相反时压电层状半空间中的B-G波

对于覆盖层与基底介质极化方向相反的压电状半空间,在自由表面电学开路和短路两种情况下,分析用解析的方法以了Ｂｌｅｕｓｔｅｉｎ－Ｇｕｌｙａｅｖ波传播的相速度方程或相速度的表达式;以工程技术中应用的压电材料为例考察了波速随覆盖厚度ｈ的变化规律,为了分析表面金属薄膜对波的传播速度的影响,计算了机电耦合系数ｋ＾２与ｈ的关系,结果表明：层状结构Ｂ－Ｇ波传播时具有很小的穿透深度,同时在ｈ取适当值时依然可使ｋ＾２     

基于谱元法考虑层间接触状态的Rayleigh波频散特征正演计算

为了提升Rayleigh波应用于成层土基勘探的精细化水平，本文基于谱元法原理，通过Goodman模型和Matsui层间滑移系数建立了可考虑层间不同接触状态的Rayleigh波理论频散方程。针对典型土基成层结构，运用谱元法和快速矢量传递解析法对比计算了层间完全连续状态下土基的Rayleigh波多阶模态频散曲线，结果显示谱元法计算结果与解析法相应结果之间的平均相对误差在0.3%以下，具有较高的计算精度。在此基础上，通过改变层间接触状态和敏感性分析，揭示了层间接触状态对Rayleigh波基阶频散特征的影响。最后，结合速度-应力有限差分数值计算，验证了谱元法计算层间不同接触状态下R波频散特征的可靠性。     

多铁性扇环截面柱体中的波传播

论文基于线性磁电弹性理论，研究了具有扇环形截面的多铁性柱形波导中的弹性波传播问题.利用波动势函数法，解析推导获得波动特征方程，进而得到弥散关系.通过算例研究了波传播的关键特性，深入分析了弥散曲线、相速度曲线和截止频率变化情况.结果显示，波的相速度和截止频率非常依赖于波导结构的扇环截面半顶角、内外径比和层合界面的弱界面系数，对于给定材料的波导结构，这些参数也是控制其弥散特性的重要影响因素.值得指出的是，在柱面应力自由的边界条件下相速度曲线中存在独特的频率带隙，而这通常是在周期结构中才会出现.     

Love waves in functionally graded piezoelectric materials

To investigate the features of Love waves in a layered functionally graded piezoelectric structure, the mathematical model is established on the basis of the elastic wave theory, and the WKB method is applied to solve the coupled electromechanical field differential equation. The solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate. The dispersion relations of Love waves are deduced for electric open and short cases on the free surface respectively. The actual piezoelectric layer–elastic substrate systems are taken into account, and some corresponding numerical examples are proposed comparatively. Thus, the effects of the gradient variation about material constants on the phase velocity, the group velocity, the coupled electromechanical factor and the cutoff frequency are discussed in detail. So the propagation behaviors of Love waves in inhomogeneous medium is revealed, and the dispersion and the anti-dispersion are analyzed. The conclusions are significant both theoretically and practically for the surface acoustic wave devices.     

Complex surface rays associated with inhomogeneous skimming and Rayleigh waves

The Rayleigh wave, that propagates at the free surface of semi-infinite anisotropic medium, is composed of three inhomogeneous partial waves, each propagating along the surface with a different attenuation along the depth. Since this wave does not exhibit an attenuation on the surface, let us call it the homogeneous Rayleigh wave. The associated slowness corresponds to the real solution of the Rayleigh dispersion equation. Besides this classical solution, an infinite number of complex solutions of the Rayleigh dispersion equation exits. For such particular Rayleigh waves, the slowness vector, i.e. the identical component on the surface of the slowness of each partial waves, is taken to be complex. Thus, these Rayleigh waves are attenuated on the surface and as shown here, their attenuation is normal to the ray direction (or the energy velocity direction). Similarly to the infinite inhomogeneous plane waves which can be associated with complex rays, we call these waves, inhomogeneous Rayleigh waves. We use the inhomogeneous skimming waves, which are inhomogeneous plane waves, and the inhomogeneous Rayleigh waves to explain differently the usual diffraction phenomena on the free surface which cannot be explained by the real ray theory. For example, the arrival time of the wave packet observed beyond the cusp is in perfect accordance with the arrival time of some specific inhomogeneous Rayleigh waves. We show that these results are in agreement with the computation of the Green function. They apply to the theory of surface waves in linear elastodynamics with intrinsic anisotropy as well as to the theory of surface waves in linearised (incremental) elastodynamics with strain-induced anisotropy (also known as small-amplitude waves superimposed on the large static homogeneous deformation of a non-linear solid).     

Propagation of Rayleigh waves on curved surfaces

The propagation and properties of Rayleigh waves on curved surfaces are investigated theoretically. The Rayleigh wave dispersion equation for propagation on a curved surface is derived as a parabolic equation, and its penetration depth is analyzed using the curved surface boundary. Reciprocity is introduced to model the diffracted Rayleigh wave beams. Simulations of Rayleigh waves on some canonical curved surfaces are carried out, and the results are used to quantify the influence of curvature. It is found that the velocity of the surface wave increases with greater concave surface curvature, and a Rayleigh wave no longer exists once the surface wave velocity exceeds the bulk shear wave velocity. Moreover, the predicted wave penetration depth indicates that the energy in the Rayleigh wave is transferred to other modes and cannot propagate on convex surfaces with large curvature. A strong directional dependence is observed for the propagation of Rayleigh waves in different directions on surfaces with complex curvatures. Thus, it is important to include dispersion effects when considering Rayleigh wave propagation on curved surfaces.     

Squirt-Flow in Fluid-Saturated Porous Media: Propagation of Rayleigh Waves

Propagation of attenuated waves is studied in a squirt-flow model of porous solid permeated by two different pore regimes saturated with same viscous fluid. Presence of soft compliant microcracks embedded in the grains of stiff porous rock defines the double-porosity formation. Microcracks and pores respond differently to the compressional effect of a propagating wave, which induces the squirt-flow from microcracks to pores. Elastodynamics of constituent particles in porous aggregate is represented through a single-porosity formulation, which involves the frequency-dependent complex moduli. This formulation is deduced as a special case of double-porosity formation allowing the wave-induced flow of pore-fluid. This squirt-flow model of porous solid supports the attenuated propagation of two compressional waves and one shear wave. Superposition of these body waves, subject to stress-free surface, defines the propagation of Rayleigh wave. This wave is governed by a complex irrational dispersion equation, which is solved numerically after rationalising into an algebraic equation. For existence of Rayleigh wave, a complex solution of the dispersion equation should represent a leaky wave, which decays for propagation along any direction in the semi-infinite medium. A numerical example is solved to analyse the effects of squirt-flow on phase velocity, attenuation and polarisation of the Rayleigh waves, for different combinations of parameters. Numerical results suggest the existence of an additional (second) Rayleigh wave in the squirt-flow model of dissipative porous solids.     

Localization of wave motions in a fluid-filled cylinder

The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic, and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in hard and compliant materials of the cylinder __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 72–86, April 2008.     

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.     

Propagation of SH waves in an irregular monoclinic crustal layer

The present paper discusses the dispersion equation for SH waves in a monoclinic layer over a semi-infinite elastic medium with an irregularity. In the absence of the irregularity, the dispersion equation reduces to standard dispersion equation for SH waves in a monoclinic layer over an isotropic semi-infinite medium. The dispersion curves for different size of the irregularity are computed and compared for the half-space without any irregularity. It can be seen that the phase velocity is strongly influenced by the wave number and the depth of the irregularity.     

薄膜涂层材料中的广义瑞利波

基于弹性动力学的线性理论，建立了涂层材料中广义瑞利波传播的理论分析模型，并 且由波动方程和边界条件推导了波的频散方程．分析了慢层和快层对相速度频散的影响，给 出了不同层厚-波长比和不同涂层-基体密度比情况下广义瑞利波相速度的理论解．算例分 析分别比较了慢层和快层结构中波的相速度、群速度，以及随深度衰减的位移与应力振 幅．另外，相速度曲线和位移振幅曲线与文献中给出的结果吻合，验证了理论模型和分析过 程的正确性．     

曲面曲率对Rayleigh波传播特性的影响

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.     

Surface electro-elastic shear horizontal waves in a layered structure with a piezoelectric substrate and a hard dielectric layer

The existence and behaviour of surface electro-elastic shear horizontal waves in a layered structure consisting of a piezoelectric substrate of crystal class 6, 4, 6mm, or 4mm mechanically bonded at its upper surface to an elastic dielectric layer and bounded by an adjacent dielectric medium is considered when the shear bulk wave velocity in the elastic layer is greater than or equal to that in the substrate. The dispersion equation for the existence of the surface electro-elastic SH waves with respect to the phase velocity is obtained which includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The investigation of the solutions of the dispersion equation is carried out and all the possible cases of the behaviour of the surface electro-elastic SH wave depending on the electro-mechanical coefficients of the layered structure are revealed.