多层介质硬币形(Penny-Shaped)交界裂纹的弹性波散射

本文研究多层介质硬币形交界裂纹的弹性波散射.文中采用Hankel积分变换,得到了含有硬币形交界裂纹多层介质模型的散射波传递矩阵,并将散射问题为转化求解矩阵形式的对偶积分方程.作为特例,文中给出了单一弹性层与半空间的硬币形交界裂纹的弹性波散射远场模式,并计算了几组不同弹性常数组合情形下的远场模式的幅频特性曲线,其结果表明有共振峰存在.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

Some exact solutions for the propagation of transient electroacoustic waves. II: Plane interface between two piezoelectric media

Electroacoustic waves are coupled horizontal-shear (SH) and electromagnetic disturbances that propagate in certain types of piezoelectric media. At the interface between two semi-infinite piezoelectric media, a new type of electroacoustic surface wave, called a Maerfeld-Tournois wave, can exist that has no purely elastic wave counterpart. This article obtains exact transient solutions for the Maerfeld-Tournois and body waves generated by a dipole source on such an interface. These solutions are obtained for both conducting and nonconducting interfaces using a modification of the Lamb-Cagniard-Pekeris technique. In the quasistatic approximation, explicit results for all the waves present are given and the separated body and surface waves at the interface are discussed.     

On the wave transmission across the interface of two elastic half spaces with nonlocal cohesion forces

Summary Wave propagation across the interface of two elastic half-infinite media is examined assuming long-range action of cohesive forces. The nonlocal elastic moduli are first established by solving an auxiliary problem involving longitudinal waves in an infinite space. With constitutive equations determined, the conditions of continuity of displacements and of balance of forces at the interface of the media lead to the relations between the amplitudes of the incident, reflected and transmitted wave. The relations are illustrated by graphs.With 3 Figures     

Scattering of SH-waves by an interface cavity

Summary. The scattering of the SH-wave and dynamic stress concentrations near an arbitrary cavity situated at the planar interface separating two different elastic media are investigated. The total wave field can be obtained by superposition of the free field and the scattered field. The free field is composed of the incident, reflected and refracted waves. The scattered wave fields in adjacent media are expressed respectively, and the method of wave functions expansion is applied to obtain the solutions for these fields. The scattered wave functions can be expanded into Hankel-Fourier series with unknown coefficients. In solving for the unknown coefficients according to the boundary conditions for the total wave field at the interface and at the cavity wall, the non-orthogonality makes the system of equations for the unknown coefficients infinite and coupling each other. Another key point is to extend each scattered wave field from its own half-plane domain into the full plane domain by a certain way keeping the total wave field unchanged for the non-orthogonal Fourier integrals around the cavity. Finally, the scattering of the SH wave by an interface ellipse with different ratios between long and short axis is considered, and the distributions of dynamic stress concentration factors at the cavity wall are presented.     

Nonlinear wave scattering at the flexible interface of a granular dimer chain

Uncompressed granular dimer chains composed of repetitive pairs of heavy-light spherical, linearly elastic beads exhibit interesting intrinsic responses. The dynamics of these highly discontinuous nonlinear media is governed by the mass ratio scaling the mass disparity of each heavy-light pair of beads. In particular, it has been theoretically and experimentally shown that they support countable infinities of anti-resonances at a discrete set of mass ratios leading to solitary pulses propagating through the dimers with no attenuation or distortion. Conversely, they support countable infinities of resonances at a different discrete set of mass ratios, leading to substantial and rapid attenuation of propagating pulses due to energy scattering from low-to-high frequencies and wavenumbers by means of radiating traveling waves. In this work we computationally study nonlinear scattering of impeding pulses at the interface of an impulsively excited dimer chain with a dispersive elastic boundary, namely, a finite linear string resting on an elastic foundation. We develop a computational algorithm which, through iteration and interpolation at successive time steps, accurately computes (and ensures convergence of) the highly discontinuous contact forces and displacements at the flexible interface of the granular medium. This enables accurate computation of wave transmission, reflection, localization or multi-scale nonlinear scattering at the flexible interface for varying mass ratios of the dimer and the interface parameters. We show that, depending on the mass ratio of the dimer and the stiffness of the elastic foundation, the nonlinear scattering at the flexible interface may lead to significant reduction of the maximum contact force at the interface, and, thus, drastically affect the transmitted and reflected energy at the flexible boundary. In fact, an inverse relation between the stiffness of the elastic foundation and the residual energy transferred from the dimer chain to the flexible boundary is found. Moreover, for sufficiently small mass ratios of the dimer chain transient breathers are realized close to the interface in the form of localized “fast” oscillations of light granules of the dimer that entrap shock energy and then release in a slow time scale back to the chain and the flexible boundary. This work paves the way for studying highly discontinuous and nonlinear scattering phenomena at interfaces of granular media with flexible continua.     

On interface crack propagation with variable velocity for longitudinal shear problems

The antiplane strain problem of straight interface crack propagation between two elastic half-spaces under arbitrary variable loading is considered. The crack edge is specified as an arbitrary smooth function of time. It is assumed that the crack speed is less than the smaller of the shear wave velocities of two media. An integral transform method and factorization technique are used to solve the problem. The solutions are worked out for semi-infinite crack and finite crack problems. The dynamic stress intensity factors at the crack tip of the moving interface crack are given and it is found that the stress intensity factor of the interface crack is slightly higher than that in the homogeneous medium with slower shear wave velocity.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Effect of surface stress and irregularity of the interface on the propagation of SH-waves in the magneto-elastic crustal layer based on a solid semi space

The object of the present paper is to investigate plane SH waves through a magneto-elastic crustal layer based over an elastic, solid semi space under the influence of surface stress on the free surface of the crustal layer and irregularity of the interface. Two types of irregularities of the interface namely, rectangular and parabolic have been considered. Modulations of wave velocity due to the presence of surface stress, irregularity and the magnetic field have been studied separately. Their combined effect has also been investigated. Graphs are drawn to highlight some important peculiarities. It is observed that surface stress, irregularity and magnetic field have their respective role to play in the propagation of SH waves in the crustal layer. Further modulation of wave velocity occurs due to their combined effect.     

轨道交通地面振动衰减关系中局部放大现象形成机理研究

为了研究城市轨道交通引起的环境振动竖向位移衰减关系中局部放大现象的产生机理,将场地简化为弹性半空间单一覆盖层模型,采用传递矩阵法推导了频率波数域三维层状场地竖向位移的动力格林函数。通过七个半空间与覆盖层的模量比,四个覆盖层厚度,七个激励频率,三个覆盖层阻尼比等诸多因素对局部放大影响的分析,结果表明局部放大受埋藏的主要速度界面控制,局部放大区的位置和放大的强度与该界面两侧的模量比（波阻抗比）、覆盖层厚度、激励的频率及覆盖土层的阻尼比等因素有关。一般来说,速度界面的波阻抗越大,局部放大越强烈;给定其他条件,使直达的表面波与半空间表面折射波越接近同时到达的覆盖层厚度使局部放大越为明显,使两者波峰越靠近的激励频率会引起更为明显的局部放大;覆盖层阻尼比越小,局部放大越强烈。     

液浸多层薄膜-基底结构中Scholte界面波特性研究

多层薄膜-基底结构在工业领域有广泛应用，其中薄膜的厚度与弹性参数等特性对结构与器件性能有显著影响。但对多层薄膜材料参数进行无损定征较为困难。考虑界面波对界面附近材料特性敏感的特点，以及分层薄膜导致液固界面Scholte波频散与分层材料速度分布密切相关等因素，文章首先利用全局矩阵理论分析了分层结构中的声传播，并给出界面上脉冲激励的声压表达式，据此对水浸双层薄膜-基底三层结构材料声速呈正梯度、负梯度、随机分布三种结构中液固界面Scholte波的频散曲线进行数值计算。进一步详细计算了法向脉冲线源激发的界面波瞬态信号随薄膜厚度的变化。结果显示，三种结构中两层薄膜厚度均对液-固界面波频散特性有显著影响，同时不同膜厚对不同频段的Scholte波的“捕获”作用(频率选择性)十分明显。该结果为进一步利用Scholte波频散特性进行多层薄膜厚度定征提供了理论依据。     

Harmonic generation at an unbonded interface—I. Planar interface between semi-infinite elastic media

An analysis is made of the nonlinear dynamics of a system composed of an unbonded planar interface separating two semi-infinite linear elastic media. The unbonded interface, by definition, cannot support tension and hence opens up in the tension phase of a propagating disturbance, if it is not already open. The opening and closing of the interface is the origin of the nonlinearity. This is perhaps the simplest nonlinear problem involving continuous media, since the problem reduces to the consideration of a pair of independent first order ordinary differential equations involving the center of gravity and width of the gap. In the case of an incident sinusoidal wave the second harmonic generation efficiency is determined as a function of the ratio of the ambient hydrostatic pressure to the stress amplitude of the incident wave.     

基于谱方法分析有阻尼负载圆柱壳频散特性

以Chebyshev多项式系为基函数,采用谱方法离散弹性理论的波动方程,建立对应的广义特征值问题。依据壳体结构波运动、内部流体及外部阻尼材料在界面处的位移、应力连续条件,构造此复杂圆柱壳系统广义特征值方程。通过数值求解特征值获得对应频率下波数,进而获得圆柱壳结构的频散曲线。分别讨论充水与否、有阻尼负载圆柱壳的频散曲线,获得有价值结论。     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

界面剥离钢-混凝土组合结构应力波传播谱元法模拟研究

建立钢-混凝土组合结构截面二维谱元法模型,针对钢-混凝土界面完好以及存在界面剥离时模型在单点激励下弹性应力波场进行模拟分析,探究弹性应力波的传播规律。采用去除混凝土单元的方法反映组合结构中钢板与混凝土之间的界面剥离。通过对比分析表明界面剥离的存在对弹性应力波场以及模型上不同位置的位移响应产生影响。通过改变界面剥离程度,得到测点位移的变化规律。通过模拟,谱元法可以有效模拟钢-混凝土组合结构中弹性波的传播规律,为研究基于应力波测量的钢-混凝土组合结构界面缺陷检测机理提供帮助。     

Transient waves in two semi infinite viscoelastic media separated by a plane interface

We consider the reflection and transmission of a transient, cylindrical, longitudinal wave by a plane interface between two semi infinite linear viscoelastic media.The four relaxation functions are assumed to be synchronous, but no further restrictions are placed on the viscoelastic behaviour of the two materials.By means of Laplace and Fourier transformation together with Cagniard-de Hoop's way of integrating we obtain expressions for the displacement components in terms of one- or three-dimensional integrals. The integrands contain a function which in general has to be found numerically from its Laplace transform.Computations are carried out for elastic materials and for two different standard linear solids. The displacement of the incident wave is found for different radii, and at two observation points the displacement components of the reflected longitudinal wave with its faster head wave and of the reflected transverse wave are computed.     

Diffraction of SH-waves with cracks in composite media

This article addresses the problem of interaction of three co-planar finite cracks, symmetrically positioned at the interface of two bonded dissimilar elastic half spaces. The cracks are excited by anti-plane shear wave. The elastrodynamic problem has been converted into a set of four integral equations using the Fourier transform method. These set of equations have then been solved by using the finite Hilbert transform technique and Cooke’s result. The solutions are used for calculating numerical values of quantities of physical interest, such as the dynamic stress intensity factor and the crack opening displacement for low-frequency vibration, which have been presented graphically for different materials.     

Complex stress intensity factors at tips of cracks along interfaces of dissimilar media

The method of reflected caustics was used to determine the complex stress intensity factors at the tips of cracks having any shape, which lie at the interface of two dissimilar elastic media. For the evaluation of complex S.I.Fs two measurements of appropriate lengths have to be made on the caustic formed at the crack tip. These measurements allow the determination of both the absolute value and the argument of the respective stress intensity factor. The method was applied for the solution of problems which are referred to cracks at interfaces between two elastic dissimilar media. The experimental results show a good agreement between the experimental and theoretical methods of evaluating SIFs.     

Numerical modeling of the V(z) curve for a thin-layer/substrate configuration

A numerical model is presented to calculate V(z) curves for a line-focus acoustic microscope and the specimen configuration of a thin isotropic elastic layer deposited on an isotropic elastic substrate. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid, interacts with the thin-layer/substrate system. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the thin layer and the interface of the thin layer and the substrate. An electrochemical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) curves are presented for various layer thicknesses and various combinations of the elastic constants of the layer and the substrate. The oscillations of the V(z) curves are related to the modes of wave propagation in a thin layer in contact with a solid half-space on one side and a fluid half-space on the other side. Calculated V(z) curves have also been compared with experimentally obtained curves, and good agreement is observed.     

SH波入射双相介质半空间浅埋任意位置圆形夹杂的动力分析

采用Green 函数及复变函数方法研究了SH 波入射到双相介质半空间时,浅埋任意位置圆形夹杂的动力响应问题。首先,利用“镜像”法构造满足直角平面自由边界条件的散射波场解答,进而求出该文所需的Green函数;其次,利用“契合”思想,将模型沿着垂直界面剖分为两个直角域,并利用界面连续性条件及Green函数建立待解外力系的第一类Fredholm 积分方程组;最后,通过具体算例给出了圆形弹性夹杂周边的动应力集中系数。结果显示:界面、自由边界、圆形夹杂、入射波数等因素均对动应力集中系数有影响。