非线性岩土中球壳对冲击波的动力响应分析

ANALYSES OF DYNAMIC RESPONSE OF A SPHERICAL SHELL IN NONLINEAR GEO-MEDIUM TO SHOCK WAVES

采用小参数摄动法和Ｌａｐｌａｃｅ变换研究了非线性弹性岩土中球壳对冲击波的动力响应问题。系统的非线性方程由小参数摄动渐近展开后，利用Ｓｔｏｋｅｓ－Ｈｅｌｍｈｏｌｔｚ矢量分解定理把它们简化为一系列的线性波动方程，并由Ｌａｐｌａｃｅ变换和本征函数给出了各线性波动方程的求解。最后，对平面冲击波和球面冲击波给出了球壳动力响应的应力结果。

This paper deals with the dynamic response of spherical shell in nonlinear elasticgeo-medium to shock waves using the methods of small parameter perburbation and Laplace-transform. The asymptotic linear equations are derived from nonlinear ones of the system by per-burbation,and reduced to a series of decoupled linear wave equations by stokes-Helmholtz vectorresolution theorem. The analytical solutions of each wave equation are given by the eigenfunctionsand Laplace-transform. Finally , the stress results are presented for the case of plane and sphericalshock waves.