滑动界面球形夹杂对平面压缩波的散射

非理想粘结界面对多相材料力学性能的影响日益受到重视。本文研究了无限各向同性基体中的滑介面球形单夹杂对平面压缩的散射问题。夹杂与基体间的界面为非理想粘结界面,在剪应力的作用下将出现界面两侧相对滑移。假定界面相对滑动位移与界面剪应力成正比,在这种线弹簧型滑动界面条件下,通过波函数的级数展开法,获得了夹杂在基体中反射波和折射波以及应力场的解析表达式,并讨论了界面自由滑动和刚性夹杂等特例。     

双相介质半空间内椭圆夹杂对透射SH波的散射

为探究双相介质弹性半空间内椭圆弹性夹杂对透射SH波的散射问题,主要采用Green函数法、复变函数法、保角映射法和极坐标移动技术。首先,引入复变量并在复平面上运用保角映射的方法将椭圆边界映射为单位圆边界;然后,将双相介质沿垂直边界剖开分成两个四分之一空间,在剖分面上作用附加力系使SH波在垂直边界上满足位移和应力连续的条件,并构造四分之一空间内点源荷载作用下的Green函数位移场;进而,利用"契合"的思想在垂直边界上建立定解积分方程组,并利用SH波衰减的性质进行有限项截断来求解未知附加力系。最后,通过具体算例得出在不同参数情况下椭圆夹杂周边动应力集中因子分布情况。结果得知,SH波的入射角度和频率以及介质的性质对夹杂周边动应力集中分布有一定影响。     

固体介质中球形发散波的实验装置

建立了用于固体介质中球形发散波传播规律研究的实验技术 ,球形波源是当量为 0 .12gTNT和 0 .4 9gTNT的微型炸药球 ,波后粒子速度测计是圆环型电磁粒子速度计。用该实验和测量系统在有机玻璃和花岗岩中进行了大量的实验研究 ,实验的重复性很好。利用微型炸药球可在较小的样品中模拟较大比距离范围内的波传播。利用圆环型电磁粒子速度计可使输出信号幅度不受波强度因几何发散而快速衰减的影响 ,而且信号输出反映了波面上一条圆环线处介质动力学状态的综合平均结果。该技术的这些突出优点对研究固体介质 (特别是非均匀固体介质 )中球形发散波传播规律和相应的材料动力学特性研究具有重要意义。圆环型电磁粒子速度计测量技术同样适用于固体介质中圆柱形发散波的情况。     

波在双孔隙与单孔隙介质界面上的反射与透射

基于Biot理论和双重孔隙介质理论研究了弹性波在双重孔隙介质与流体饱和单一孔隙介质 界面的反射和透射问题,在界面上假定裂缝孔隙流体相对于固体骨架的位移为零,推导了反 射系数和透射系数的计算公式,数值讨论了反射系数和透射系数随入射角和频率的变化关 系. 同时,讨论了双重孔隙介质中3种压缩波(P-1, P-2和P-3波)和一种剪切波(S波) 的频散和衰减特性.     

各向异性介质的弹性波散射问题的边界元方法

本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.     

流体饱和标准线性粘弹性多孔介质中的平面波

研究了流体饱和不可压标准线性粘弹性多孔介质中平面波的传播和反射问题.在固相骨架小变形的假定下,得到了粘弹性多孔介质中波动方程的一般解,讨论了弥散关系和波的衰减特性.结果表明:在流体饱和不可压粘弹性多孔介质中,仅存在一个耦合纵波和一个耦合横波,纵波和横波的波速、衰减率等取决于孔隙流体与固相骨架间的相互作用以及固相骨架本身的粘性.同时,研究了半空间自由边界上入射波(纵波、横波)的反射问题,得到了非均匀反射波的波速、反射系数、衰减率等的表达式及其相关的数值结果.     

考虑质量耦合效应的流体饱和孔隙介质波动方程

利用混合物理论和连续介质力学的基本原理,推导了考虑质量耦合效应的流体饱和弹性孔隙介质的波动方程,并与经典的Biot波动方程进行了对比.结果表明:该文得到的方程包含了Biot波动方程的所有要素,且形式与后者基本相同.比较而言,该文推导过程具有更明确的物理意义,概念也更完整.     

流体饱和多孔隙介质波动方程多尺度反演

基于多尺度的思想,将小波多分辨分析和多尺度方法相结合,应用于流体饱和多孔隙介质孔隙率的反演。利用小波变换,将原始反问题分解为不同尺度上的一系列子反问题,并按照尺度从粗到细的顺序依次求解。在每一个尺度上,都采用稳定、收敛快的正则化高斯牛顿法求解,次一级尺度上求出的“全局最优解”作为上一级的初始解,依此类推,直到求出原始问题的真正的全局最优解。通过与传统的正则化高斯牛顿法相比较,显示了小波多尺度法是一个大范围收敛、能够有效节省计算量的方法,数值模拟的结果也表明了方法的有效性。     

SH波对界面圆柱形弹性夹杂散射及动应力集中

运用Ｇｒｅｅｎ函数法求解ＳＨ波对界面圆柱形弹性夹杂的散射。首先,给出含有半圆柱形弹性夹杂的弹性半空间表面上任意一点、承受时间谐和的出平面线源荷载作用时的位移函数。其次,取该位移函数作为Ｇｒｅｅｎ函数,推导出定解积分方程。最后,给出介质参数对界面圆柱形弹性夹杂的动应力集中系数的影响。     

横观各向同性液体饱和多孔介质中平面波的传播

基于孔隙介质的Ｂｉｏｔ理论１，研究了横观各向同性液体饱和多孔介质中平面波的传播特性。首先导出了波传播的特征方程并给出了其解析解，结果显示：有４种不同波速的平面体波传播；第一准纵波，第二准纵波，准横波和反平面横波。文中给出了波速和衰减的解析表达式，数值计算了频散曲线和衰减曲线，并讨论了各类准体波位移之间的耦合关系。     

Scattering of a plane monochromatic wave by a system of strips

Summary The diffraction of a plane wave by a general system of strips is treated by means of separation of variables. A new addition theorem for Mathieu functions is used to satisfy the boundary conditions on the strips. Numerical calculations are performed for the case of two strips lying in the same plane, the boundary conditions being grad _n =0, while the angle of incidence of the plane wave is arbitrary. The transmission coefficient for a system of two slits in a plane, perfectly conducting screen is calculated for a range of values of the parameters. An approximate expression relating the transmission coefficient for the system of two slits to the transmission coefficient for a system of a single slit is given. As the distance between the two slits is increased, the transmission coefficient for the system of two slitsvery rapidly becomes nearly identical with the transmission coefficient for a single slit.     

Action of an acoustic wave on a system of two spherical bodies in an ideal fluid

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 102–108, May, 1990.     

二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射

利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切（shearing horizontal, SH）波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂边界产生的能够自动满足直角边应力自由条件的散射波解,从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况,结果表明了算法的有效实用性。     

Scattering of a plane longitudinal wave by an elastic quarter space

We study the two-dimensional problem of the scattering of a plane longitudinal wave incident in a homogeneous, isotropic, linearly elastic quarter space. The complex-valued amplitudes of the Rayleigh waves propagating on the free surfaces are plotted versus Poisson's ratio. Also plotted are the farfield scattering patterns for Poisson's ratio $\text{μ=}\text{1}\text{4}$ and $\text{1}\text{3}$.     

Scattering of a plane harmonic SH wave by multiple layered inclusions

Scattering of a plane harmonic SH wave by an arbitrary number of layered inclusions in a half-space is investigated by using a direct boundary integral equation method. The inclusions of arbitrary shape and placement are embedded within an elastic half-space. The effects of multiple scattering, the geometry, and the impedance contrast of the materials for layered inclusions and pipes are considered in detail.     

Nonstationary spherical wave diffraction by a circular cylinder in a fluid

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 6, pp. 3–9, June, 1989.     

Scattering of plane monochromatic waves from a heterogeneous inclusion of arbitrary shape in a poroelastic medium: An efficient numerical solution

Scattering of plane longitudinal monochromatic waves from a heterogeneous inclusion of arbitrary shape in an infinite poroelastic medium is considered. Wave propagation in the medium is described by Biot’s equations of poroelasticity. The scattering problem is formulated in terms of the volume integral equations for displacements of the solid skeleton and fluid pressure in the pore space in the region occupied by the inclusion. An efficient numerical method is applied to solve these equations. In the method, Gaussian approximating functions are used for discretization of the problem. For regular node grids, the matrix of the discretized problem has Toeplitz’s properties, and the Fast Fourier Transform technique can be used for the calculation of matrix–vector products. The latter accelerates substantially the process of iterative solution of the discretized problem. For material parameters of typical sedimentary rocks, the system of differential equations of poroelasticity contains a differential operator with a small parameter. As the result, the wave field in the inclusion region is split up into a slowly changing part, and boundary layer functions concentrated near the inclusion interface. The method of matched asymptotic expansions is used for the numerical solution in this case. For a spherical inclusion, the results of the numerical and matched asymptotic expansion methods are compared with a semi-analytical series solution. For a non-spherical heterogeneous inclusion, an example of the numerical solution is presented.     

Scattering of a longitudinal wave by a circular crack in a fluid-saturated porous medium

Physical properties of many natural and man-made materials can be modelled using the concept of poroelasticity. Some porous materials, in addition to the network of pores, contain larger inhomogeneities such as inclusions, cavities, fractures or cracks. A common method of detecting such inhomogeneities is based on the use of elastic wave scattering. We consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical co-ordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave induced fluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has it’s maximum value when they are of the same order.     

The problem of a gas bubble in plane ideal fluid flow

We study the problem of two-dimensional fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall.Two-dimensional ideal fluid flow past a gas bubble on whose boundary surface-tension forces act (or a gas bubble bounded by an elastic film) has been studied by several authors. Zhukovskii, who first studied jet flows with consideration of the capillary forces, constructed an exact solution of the problem of symmetric flow past a gas bubble in a rectilinear channel [1]. However, Zhukovskii's solution is not the general solution of the problem; in particular, we cannot obtain the flow past an isolated bubble from his solution. Slezkin [2] reduced the problem of symmetric flow of an infinite fluid stream past a bubble to the study of a nonlinear integral equation. The numerical solution of this problem has recently been found by Petrova [3]. McLeod [4] obtained an exact solution under the assumption that the gas pressure p₁ in the bubble equals the flow stagnation pressure p₀. Beyer [5] proved the existence of a solution to the problem of flow of a stream having a given velocity circulation provided p₁p₀.We examine the problem of two-dimensional ideal fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. The solution depends on the value of the contact angle . The existence of a solution is proved in some range of variation of the parameters, and a technique for finding this solution is given. The situation in which =1/2 is studied in detail.     

Scattering of a pulsed Rayleigh wave by a spherical cavity in an elastic half space

The time-dependent scattering by a spherical cavity in an elastic half space is considered. The incoming wave is a pulsed Rayleigh wave. The stationary part of the problem is solved by the T-matrix method, and an integration in frequency is performed with a modified gaussian weight function. The displacement components at some points on the surface of the half space are computed and shown in a number of plots.