倾斜界面耦合弹性层中的渡越辐射能

物理学中,摄动源在非均匀介质中或非均匀介质附近匀速直线运动所产生的能量辐射现象称为渡越辐射.列车沿轨道运行,由轮轨接触产生的弹性波在非均匀轨道和基础中传播将发生渡越辐射,而轨道和基础的非均匀性集中体现在不同轨道基础之间的过渡段(如路桥过渡段、桥隧过渡段或有砟-无砟轨道过渡段).为研究车致弹性波在过渡段中引发的渡越辐射现象,本文以典型高速铁路路桥过渡段结构形式为依据,建立了二维平面应力渡越辐射能计算模型.其中,两个材料参数不同的半无限弹性层由一倾斜界面耦合,底端固定,上表面自由,一个集中载荷在自由表面上匀速运动.界面两侧弹性体中的波动方程均分解为本征场、自由场两个部分分别求解,其中自由场波动方程采用分离变量法数值求解.通过模型求解得到了不同载荷移动速度和界面倾斜角度条件下的渡越辐射能及界面附近应变能密度.结果表明,渡越辐射能的大小随载荷移动速度增大单调非线性增大,移动载荷速度达到刚度较大一侧介质表面波速的74%时产生的渡越辐射能就将超过载荷本身激发的本征场应变能;界面倾斜角度越大,即两侧介质刚度过渡距离越短,渡越辐射能与本征场应变能比值越大.     

倾斜界面耦合弹性层中的渡越辐射能

物理学中,摄动源在非均匀介质中或非均匀介质附近匀速直线运动所产生的能量辐射现象称为渡越辐射.列车沿轨道运行,由轮轨接触产生的弹性波在非均匀轨道和基础中传播将发生渡越辐射,而轨道和基础的非均匀性集中体现在不同轨道基础之间的过渡段(如路桥过渡段、桥隧过渡段或有砟-无砟轨道过渡段).为研究车致弹性波在过渡段中引发的渡越辐射现象,本文以典型高速铁路路桥过渡段结构形式为依据,建立了二维平面应力渡越辐射能计算模型.其中,两个材料参数不同的半无限弹性层由一倾斜界面耦合,底端固定,上表面自由,一个集中载荷在自由表面上匀速运动.界面两侧弹性体中的波动方程均分解为本征场、自由场两个部分分别求解,其中自由场波动方程采用分离变量法数值求解.通过模型求解得到了不同载荷移动速度和界面倾斜角度条件下的渡越辐射能及界面附近应变能密度.结果表明,渡越辐射能的大小随载荷移动速度增大单调非线性增大,移动载荷速度达到刚度较大一侧介质表面波速的74%时产生的渡越辐射能就将超过载荷本身激发的本征场应变能;界面倾斜角度越大,即两侧介质刚度过渡距离越短,渡越辐射能与本征场应变能比值越大.      

气饱和与水饱和多孔介质的弹性波场数值模拟

基于Biot介质理论,对气饱和多孔介质与水饱和多孔介质中弹性波的传播进行了数值模拟.通过饱和多孔介质的一阶双曲型速度-应力弹性波波场分离方程,采用交错网格高阶有限差分法实现了气饱和与水饱和介质中的高精度数值模拟,并利用完全匹配层(PML)吸收边界来处理边界反射问题,取得了较好的效果.模拟实例表明,水饱和介质中快纵波速度要远高于气饱和介质中的速度,并且频散较小,衰减较弱;含水饱和夹层的气饱和介质对弹性波振幅、能量有减弱作用;且气固耦合作用比水固耦合作用要小,气饱和情况下流相与固相基本达到完全解耦.     

多层圆柱体锚固结构中超声导波频散特征的研究

超声导波无损检测技术因其高效和快捷的优点成为检测锚杆锚固质量的有效方法。但锚固锚杆结构中超声导波的多模态性、频散性与能量泄露导致完整的锚杆底端反射信号的获得具有不确定性。应用弹性动力学理论并采用全局矩阵法建立超声导波在多层圆柱体锚固结构中的频散方程的通用表达式,然后通过非线性外推法和二分法两步算法求解频散方程的精确解,解决了频散曲线的分类和相交等难题,获得了具有自主知识产权的求解多层圆柱体锚固结构频散曲线的程序。利用该程序计算了不同锚固锚杆结构的频散曲线,并与商用软件Disperse计算的结果吻合较好。同时用本程序计算了实验室有限锚固结构中的频散曲线,验证了低频导波在有限与无限结构中的巨大差异,而这一结构特征的频散特性Disperse并未给出相关算例。     

基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。     

弹性带形域中多个半圆柱形凹陷对SH波的散射

对稳态SH（shear horizontal）导波在表面含有多个半圆柱形凹陷的弹性带形介质内的散射问题进行了研究，并给出了解析解。首先，运用导波展开法构造平面SH导波；然后，利用累次镜像法构造出满足带形域上、下两条直边界应力自由条件的散射波；最后，根据凹陷边沿的切应力为零的条件得到定解方程。通过算例分析了累次镜像法的精度、凹陷边沿的动应力集中和上、下边界位移幅值的变化情况。数值结果表明:只有一个凹陷时，中高频率的入射波和小厚度的带形域会引起凹陷边沿更高的动应力集中，上边界位移幅值的最大值会出现在凹陷的迎波面附近；当有两个凹陷时，大多数情况下，第二个凹陷对第一个凹陷边沿的动应力集中起放大作用，并且在理想弹性带形介质内，两凹陷之间的影响在相距无穷远时也会存在。     

弹性波散射与多重散射的T矩阵方法

研究弹性波散射与多重散射的T矩阵方法。首先,基于Helmholtz体内和体外公式推导了对应于圆柱型散射体的T矩阵元素的具体表达式;接着分析了在含多个随机分布圆柱型散射体的随机非均匀介质中弹性波的多重散射并给出在统计平均意义下的相干波的定义以及波速和衰减系数计算公式;最后,针对Ge/Al、Sic/Al复合材料用Matlab进行了编程和数值计算;计算单个柱型散射体的散射截面以及随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。     

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.     

注浆锚杆中扭转导波的传播特性

理论研究了扭转导波在注浆锚杆中的传播特性。首先建立了注浆锚杆两层复合结构中的扭转导波的频散方程,之后数值计算得到了扭转导波的能量速度、衰减频散曲线及导波在注浆锚杆中的位移分布情况。结果表明,(1)500kHz范围内,注浆锚杆中具有三种扭转导波模态T(0,1)~T(0,3),三种模态均具有频散性。随着频率逐渐增大,导波的能量速度逐渐增大,而衰减值逐渐减小。(2)50kHz和200kHz的T(0,1)模态扭转导波在锚杆体内的周向位移值较大,所以对锚杆体表面的轴向缺陷敏感,而导波在锚杆与注浆体接触面上的周向位移较大,从锚杆泄漏至注浆体中的能量较大,导波衰减较严重。(3)频率高于100kHz,锚杆直径的变化对T(0,1)模态的能量速度几乎无影响,而频率低于100kHz,注浆体弹性模量越大,T(0,1)模态的能量速度越小。     

裂隙挤喷流对孔隙介质排水体积模量的影响

实际岩石比如沉积形成的岩石往往是裂隙和孔隙并存的孔隙介质. 由于扁状的裂隙与近似球形或圆管形的孔隙具有不同的可压缩性,当孔隙介质受压时,液体会从易压缩的裂隙中挤出流入不易压缩的孔隙中,这种挤喷流会引起弹性模量的频散和能量的耗散. 着重研究了裂隙挤喷流和液体可压缩性对孔道变形的影响,推导出了动载荷作用下排水体积模量的表达式. 与挤喷流相关的裂隙附加柔度会引起排水体积模量随频率变化,使得孔隙介质呈现黏弹性. 频率越高,模量的实部越大,岩石抵抗变形的能力越强. 而模量的虚部体现了挤喷流对能量的耗散. 裂隙密度主要决定模量频散的幅度以及能量耗散的强度,且裂隙密度越大,模量频散幅度越大,能量耗散也越强. 裂隙的纵横比主要决定模量频散速率最快或能量耗散最强时对应的特征频率. 若孔隙介质中不含有裂隙,即裂隙密度是0时,排水体积模量退化为Biot理论中的排水体积模量.     

DYNAMIC RESPONSE OF A DOUBLE-LAYERED SUBGRADE WITH ROCK SUBSTRATUM TO A MOVING POINT LOAD

In this paper, an analytical solution for the dynamic response of a double-layered subgrade with rock substratum to a moving point load is derived. The subgrade profile is divided into two layers. The upper layer is modeled by an elastic medium and the lower layer by a fully saturated poroelastic medium governed by Biot’s theory. In the meanwhile, the subgrade is resting on the rock substratum. The analytical solutions for stress, displacement and pore pressure are derived by using the Fourier transform. Numerical results obtained by using the inverse fast Fourier transform (IFFT) are used to analyze the influence of the moving load velocity, the thickness of an elastic medium layer and a fully saturated poroelastic medium layer on the dynamic response.     

Instability of a compressed elastic film on a viscous layer

A flat, compressed elastic film on a viscous layer is unstable. The film can form wrinkles to reduce the elastic energy. A linear perturbation analysis is performed to determine the critical wave number and the growth rate of the unstable modes. While the viscous layer has no effect on the critical wave number, its viscosity and thickness set the time scale for the growth of the perturbations. The fastest growing wave number and the corresponding growth rate are obtained as functions of the compressive strain and the thickness ratio between the viscous layer and the elastic film. The present analysis is valid for all thickness range of the viscous layer. In the limits of infinitely thick and thin viscous layers, the results reduce to those obtained in the previous studies.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

Analysis of micro-structural effects on phononic waves in layered elastic media with periodic nonsmooth coordinates

Propagation of elastic phononic waves in layered composite materials is analyzed by introducing nonsmooth periodic coordinates associated with structural specifics of the materials. Spatial scales of the original (smooth) coordinates are estimated by the wave lengths. In terms of the new coordinates, the homogenization procedure occurs naturally from the continuity conditions imposed on elastic displacements and forces at layer interfaces. As a result, higher-order asymptotic approximations describing spatiotemporal ‘macro’- and ‘micro’-effects of wave propagation are obtained in closed form. Such solutions provide visualizations for the wave shapes illustrating their structure induced local details. In particular, beat-wise mode shapes and effective anisotropy of acoustic wave propagation are revealed. The subharmonic beating in wave modes occur when wave lengths orthogonal to layers is about to ‘resonate’ with layer’ thickness. If the wave speed has a non-zero projection along the layers, then phase shifts between the beats are observed in different cross sections perpendicular to the layers.     

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer–Viscous-Liquid-Layer System

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier–Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.     

Wave dispersion in randomly layered materials

Wave scattering in materials composed of two kinds of alternating layers with different elastic properties and randomly distributed thicknesses has been modeled. The general form of the dispersion equation is derived for the unbounded layered medium. It defines two basic macroscopic characteristics of the scattered wave: phase velocity and attenuation, which are explicit functions of wave frequency and microscopic parameters of the system: acoustic properties of the layers and stochastic characteristics of their thickness distributions. The analytical expressions are derived for three special cases: for long waves; for a periodic medium composed of layers with constant thicknesses and for random medium with uniform distribution of layer thicknesses. Special attention is paid to the analysis of the frequency dependence of the wave parameters. It was shown that the predictions of the model for long waves and for periodic medium are compatible with the results obtained in the literature.Moreover, comparison of theoretical results for frequency dependent wave parameters with numerical simulations of pulse transmission through the slab of the randomly layered medium shows good qualitative and quantitative agreement in wide frequency range.     

THE AXISYMMETRIC MIXED BOUNDARY-VALUE PROBLEM OF THE VERTICAL VIBRATION OF A RIGID FOUNDATIONON SATURATED LAYERED SOIL SUBGRADE

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Cutting-off effect at reflection–transmission of acoustic waves in anisotropic media with sliding-contact interfaces

The specific feature of the interface, which maintains sliding contact between elastic media, is that it can be impervious to the wave field existing in one of the adjoined materials. As a result, reflection–transmission of plane acoustic waves at the sliding-contact interface may enjoy the cutting-off effect, which implies that neither bulk, nor inhomogeneous modes are being transmitted at particular angles of incidence. The necessary and sufficient criteria for this phenomenon are obtained for a binary structure, constituted by two elastic half-spaces in sliding contact, and for a sandwich structure with sliding-contact interfaces between the enclosed layer and the substrates. In the generic case of unrestricted anisotropy (triclinic materials), the criterion for cutting-off in a binary structure involves acoustic parameters of solely that of the half-spaces, which contains the incident mode, and proves to be independent of an adjacent medium. The frequency-dispersive criterion for the absence of transmission through a triclinic layer in the sliding-contact sandwich structure is independent of substrates. By appeal to the Stroh formalism, the cutting-off conditions in a binary and a sandwich structure are further elaborated under the assumption that one of the half-spaces, or a layer, is orthorhombic, and its two symmetry planes are parallel, respectively, to the plane of incidence and to the sliding-contact interface with arbitrary adjacent media. It is shown that the transmission cut-off in a binary structure is necessarily accompanied by the absence of mode conversion at reflection, but the reverse is not true. The angles of incidence which give rise to these effects are determined in terms of elastic coefficients. Transmission cut-off through an orthorhombic layer comes about at an arbitrary angle of incidence, related to guided-modes range in the layer, for the corresponding aperiodic infinite set of the frequency values. Relations for the coefficients of reflection and transmission at the sliding-contact interface between two orthorhombic half-spaces are obtained in concise form, expressed solely via normal components of the partial Stroh-normalized traction amplitudes. Provided that the adjoined orthorhombic half-spaces in sliding contact are identical, the same value of wave-vector tangential projection, which stipulates transmission cut-off at the incidence of, say, the fast mode, entails total transmission at the incidence of the slow mode.     

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted microbeam on Pasternak foundation is investigated. The strain-displacement relations (kinematic equations) are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory (SGT) is used to implement the size dependent effect at microscale. Finally, using an energy method and Hamilton’s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave propagation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is inversely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.