位移阶跃SH波对半圆形凹陷地形的散射

本文利用积分变换和波函数展开方法求解位移阶跃的平面ＳＨ波对半圆形凹陷地形的散射问题,导出了散射位移场的解析表达式,,并给出了在凹陷地形表面上各点位移时程反应的数值结果。本文的结果可做为Ｄｕｈａｍｅｌ积分的影响系数求解一个随时间任意变化的平面ＳＨ波被半圆形凹陷地形散射的问题。     

直角平面角点衬砌对稳态平面SH波的散射

利用波函数展开法求解了二维直角平面角点处圆弧形衬砌对稳态入射平面SH波的散射问题,得到问题的解析解．方法是首先构造出衬砌介质内外的总波场,它们能够预先满足直角平面两直角边界应力自由条件;再利用衬砌边界处的应力和位移连续条件写出确定散射波解中未知系数的方程组并求解．通过算例具体讨论了衬砌内边界处的环向应力集中系数和位移幅度比随无量纲波数、入射角的变化情况,结果表明它们存在不同程度的放大现象．     

弹性半空间中含直边界半圆形衬砌隧道对SH波的散射解析解

为进一步揭示含直边界衬砌隧道对SH波散射的影响,根据弹性波动理论,结合\"分区契合\"思想,建立了弹性半空间中半圆隧道对波场散射问题的波动方程.利用傅里叶级数展开的方法,引入辅助函数和波函数展开技术,通过对连续性条件和边界条件的分析,求得半空间中含直边界衬砌隧道对SH波散射的封闭解析解.计算结果表明:入射波特性、半圆隧道衬砌材料特性、隧道埋置深度对地表位移幅值影响显著;对于软性和硬性衬砌隧道而言,当频率逐渐增大时,地表位移幅值也随之增大,地表位移幅值空间振荡更为剧烈;随着入射角度增大,地表位移幅值整体上呈减小趋势;随着隧道埋深d/a由2增加到5时,隧道上方地表位移幅值降幅显著.     

楔形空间中任意形状孔洞对平面SH波的散射：IBEM求解

采用间接边界元法(IBEM),求解了楔形空间中任意形状孔洞对平面SH波的散射问题。基于单层位势理论,首先在孔洞表面及其附近楔形空间表面上施加虚拟均布荷载,以构造散射波场。进而由自由表面零应力条件,建立方程求解得到虚拟荷载密度。总波场由楔形空间自由波场和散射波场叠加得到。研究表明：IBEM方法能够精确高效求解楔形空间中弹性波散射问题。楔形空间孔洞对波的散射特征依赖于波入射角、无量纲入射波频率、楔形夹角、孔洞位置及其形状;孔洞周围波的相干效应十分显著,空间表面位移幅值及孔边动应力集中因子比半空间情况放大一倍有余,分别达到8.5和10.0;该研究为楔形空间中更为复杂的P、SV波散射问题求解奠定了基础。     

SH波绕界面孔的散射

用波函数展开方法研究了SH波绕界面孔的散射问题。由入射、反射和透射波组成的自由波场与孔的散射场叠加成总波场。按照一定方式将两个半平面散射波场延拓于全平面,通过Hankel-Fourier展开方法求得了任意形状孔散射场的级数解。以椭圆形孔为例计算了孔边缘的动应力集中系数。     

圆弧形层状沉积谷地对入射平面SV波散射解析解

利用Fourier-Bessel级数展开法给出了圆弧形层状沉积谷地对入射平面SV波散射问题的一个解析解,并分析了谷中层状沉积排列顺序及相对刚度等因素对散射的影响.     

界面圆孔对SH波散射的远场解

采用格林函数方法研究界面圆孔为ＳＨ波散射的远场解答,在构造格林函数并求解界面圆孔对ＳＨ波散射及其近场解答的基础上,继续研究该问题的散射远场,给出了散射波远场位移模式和散射截面的解答,通过具体算例,分析了不同材料组合而成的界面圆孔对ＳＨ波散射的远场特性。     

SH波对直角平面区域内圆形衬砌的散射与地震动

研究了以任意方向入射的平面SH 波对直角平面区域内圆形衬砌的散射与地震动问题．利用复变函数法、多极坐标移动技术及镜像法,将直角平面区域内的波场延拓于半无限空间,根据边界条件将该问题的解答可归结为对一组无穷代数方程组的求解问题,通过算例考虑衬砌的动应力集中和地表位移．结果表明,衬砌的动应力集中和地表位移幅值取决于入射波频率、角度、衬砌的位置和厚度比．     

圆弧形凹陷地形表面覆盖层对入射平面P波的影响

利用Fourier-Bessel级数展开法给出了表面具有覆盖层的圆弧形凹陷地形对入射平面P波散射问题的一个解析解,并利用该解分析了不同形状凹陷地形表面覆盖层刚度和厚度对入射P波的影响. 结果表明,凹陷地形表面覆盖层的存在,即使厚度很薄,对入射P波的散射也具有很大影响,覆盖层刚度和厚度的变化可显著改变凹陷地形场地的动力特性.     

SH波对浅埋裂纹的半圆形凹陷地形的散射

采用Green函数方法，研究浅埋裂纹和含有圆形凹陷的弹性半空间对入射SH波的散射。首先取含有半圆形凹陷的弹性半空间，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基本解作为Green函数；然后求解含半圆形凹陷的弹性半空间对SH波的散射问题；最后在裂纹实际存在位置利用Green函数实施裂纹的人工切割以恢复存在的裂纹，给出浅埋裂纹的半圆形凹陷弹性空间内的位移函数，进而求解裂纹存在对地表位移的影响。     

Diffraction of Plane Sound Waves on a Hard-Soft Half-Plane

A simple method is proposed for solving the problems of diffraction of plane sound waves on a half-plane with different-type boundary conditions on its surfaces (the Neumann condition on one surface and the Dirichlet condition on the opposite surface). In contrast to existing techniques, the proposed method allows one to obtain analytical solutions valid near the half-plane edge and at far distances from the edge.     

Diffraction of Surface Waves by the Edge of a Wedge

Conditions of propagation of Rayleigh waves over an elastic wedge are considered. Refraction factors are determined for conversion of the initial wave into secondary volume and surface waves. Calculation results for the modules of the refraction coefficient agree well with published experimental data.     

多圆孔圆板问题的数值解

提出了一种求解多圆孔圆板问题的新方法。首先引入了基本特解，它由主要部分和附加部分组成。主要部分为带奇点无限平板的一个特殊弹性力学解，奇点取在内圆孔的中心处。附加部分为实心圆饭的一个特解。整个基本特解满足外圆周界为自由条件。文中把待求解取为特解系的形式，其中待定系数可用变分原理得出。最后给出了算例。     

Establishment of Surface Waves Generated by Hydrodynamic Singularities in Plane Flow

A method of direct proof of the existence of steady-state regimes in classical problems of small waves on the surface of a plane flow of ideal heavy fluid of infinite depth accompanying the uniform motion of a hydrodynamic singularity inside the flow or the operation of a pulsating immersed source is proposed.     

Generation of the Third Harmonics by Plane Waves in Murnaghan Materials

We demonstrate that it is expedient to use the complete expansion of the potential in terms of strain gradients for materials whose deformation is described by Murnaghan's potential. The cubic terms are retained in the constitutive equations, in addition to the classical quadratic terms. An analysis of the nonlinear system of wave equations reveals that the third harmonics can be generated. As an example, the nonlinear interaction of plane waves is analyzed for the following three cases of waves entering a medium: (i) a longitudinal wave, (ii) a vertically polarized transverse wave, and (iii) vertically and horizontally polarized transverse waves     

Radiation and Diffraction of Water Waves by a Submerged Body with Ice Cover in Finite Depth

This paper presents the three-dimensional Green-function method to predict the radiation and diffraction of water waves by a submerged body in water of uniform finite depth with an ice cover. The fluid is assumed to be perfect and irrotational, the ice is modelled as an elastic plate. The zero-speed Green function of finite depth satisfying the linearized covered-surface condition is derived in three dimensions, the numerical results for the Green function and its derivatives are given. The integral equations are established by distributing the source strength on the body surface, the radiation and diffraction problems are solved. A submerged sphere is taken as an example, the effects of the water depth and the flexural rigidity of ice cover on hydrodynamics are analysed, and the good agreement with the analytical solutions reveals that the present method is correct and reliable.

     

Plane Problem of Surface Wave Diffraction on a Floating Elastic Plate

The problem of the behavior of a floating elastic strip-shaped plate in waves is considered. A new numerical method for solving this problem based on the Wiener-Hopf technique is proposed. The solution of the boundary value problem is reduced to an infinite system of linear algebraic equations which satisfies the reduction conditions. The calculation results are compared both with experiment and with the calculations of other authors. In the case of short incident waves the system of equations obtained can be essentially simplified. Three short-wave approximations are proposed, namely, the single-mode, four-mode and uniform approximations, which ensure good agreement with calculations based on the complete model. Simple explicit formulas are obtained for the single-mode and uniform approximations.     

Existence of a Solution for a Nonlinearly Elastic Plane Membrane Subject to Plane Forces

The two-dimensional nonlinear ‘membrane’ equations for a plate made of a Saint Venant–Kirchhoff material have been justified by D. Fox, A. Raoult and J.C. Simo (1993) by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of R³, is equivalent to finding the critical points of a functional whose nonlinear part depends on the first fundamental form of the unknown deformed surface. We establish here a local existence result for these equations in the case of the membrane subject to forces parallel to its plane and we give qualitative properties of the solutions found in this fashion in terms of injectivity and of minimization. This revised version was published online in August 2006 with corrections to the Cover Date.