各向异性介质中的Green函数解

本文首先指出Ｗａｎｇ与Ａｃｈｅｎｂａｃｈ和Ｈａｎｙｇａ关于任意各向异性，不均匀（但性质渐变）的线弹性介质中的Ｇｒｅｅｎ函数解并非完备解，而是高频条件下的近似解，并以较简洁的步骤及三维Ｒａｄｏｎ变换，得到比文献（１），（２）更合理的Ｇｒｅｅｎ函数在高频近似下显示解。在此基础上具体讨论物均匀，横观各向同性介质中的Ｇｒｅｅｎ函数完备解。

ON GREEN FUNCTION SOLUTION FOR ANISOTROPIC SOLIDS

In this paper, it points out that the Green function solution for arbitrarily anisotropic inhomogeneous (but with gradually changing properties) linearly elastic solids given by Wang and Achenbach and Hanyga is not a complete solution, being rather an approximate solution under condition of high frequency. In the paper, the author with simplified steps, applying the 3D Radon transform technique ,has obtained the explicit form of the complete solution of Green function in the sense of high frequency approximation, which is more resonable than those of in (l) and (2). On this basis, a discussion about the complete solution of the Green function for homogeneous, transversely isotropic medium is given.