Rayleigh and Stoneley Waves in Linear Elasticity

The transmission problem in linear isotropic elasticity

We study the isotropic elastic wave equation in a bounded domain with boundary with coefficients having jumps at a nested set of interfaces satisfying the natural transmission conditions there. We analyze in detail the microlocal behavior of such solution like reflection, transmission and mode conversion of S and P waves, evanescent modes, Rayleigh and Stoneley waves. In particular, we recover Knott's equations in this setting. We show that knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the P and the S waves if there is a strictly convex foliation with respect to th…

非线性弹性表面波的几何光学

Geometric optics for surface waves in nonlinear elasticity

本文研究半空间非线性弹性力学方程的高频解。我们考虑表面波（或更准确地说，瑞利波）产生的一般类各向同性超弹性模型，其中特别包括圣维南基尔霍夫系统。自20世纪80年代以来，许多作者已经完成了关于非线性发展方程的制定和适定性的工作，该方程的（精确）解给出了基础弹性方程的\emph{approximate}瑞利波解的首项。这个发展方程，我们称之为“振幅方程”，是一个非局部Burgers型的积分微分方程。我们首先回顾并提供振幅方程理论的一些扩展。本文的其余部分是致力于一个严格的证明，在2D的精确，高振荡，瑞利波解决方案$u^\eps$的非线性弹性方程存在于一个固定的时间间隔独立的波长$\eps$，和近似瑞利波解的振幅方程的分析提供的确实是在一个精确的意义上接近$u^\eps$的时间间隔独立的$\eps$。本文主要集中在瑞利波的情况下，是\emph{pulses}，它具有连续傅立叶频谱的轮廓，但我们的方法同样适用于波列的情况下，其傅立叶频谱是离散的。

Geometric optics for Rayleigh wavetrains in d-dimensional nonlinear elasticity

A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been done on the problem of constructing a leading term in an \emph{approximate} solution to the rather complicated second-order quasilinear hyperbolic boundary value problem with fully nonlinear Neumann boundary conditions that governs the propagation of Rayleigh waves. The question has remained open whether or not this leading term approximate solution is really close in a precise sense to the exact solution of the governi…

一般线弹性力学中的Rayleigh型表面准模

Rayleigh-type Surface Quasimodes in General Linear Elasticity

瑞利型表面波对应的特征品种，在椭圆形边界区域，位移牵引映射。本文构造了具有牵引力-自由边界的各向异性约化弹性波动方程的表面拟模。假设Barnett和Lothe条件的一个全局变量，构造问题归结为边界上一个自伴标量一阶伪微分算子的本征值问题.计算该运算符的主符号和次主符号。次主符号的公式似乎是新的，即使在各向同性的情况下。