非均匀介质中弹性波动方程的参数摄动法<sup>*</sup>

牛玉清; 马兴瑞; 黄文虎

非均匀介质中弹性波动方程的参数摄动法^*

哈尔滨工业大学航天工程与力学系, 哈尔滨 150001

基金项目: * 国家重点自然科学基金;国家教委博士点基金;国家教委跨世纪优秀人才计划资金

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出版历程
- 收稿日期: 1996-01-22
- 刊出日期: 1997-07-15

The Parameter Perturbation Method on Elastic Wave Equation in inhomogeneous Medium

Harbin University of Technology, Harbin 150001, P. R. China

摘要

摘要: 本文通过对非均匀介质弹性波动方程中的介质参数引入背景场量和摄动量,得到以摄动项为次生源的均匀介质中的波动方程,利用Green函数理论化微分方程为积分方程;然后把均匀介质中的位移波场做为第一次迭代结果,代入积分方程进行位移波场的求解;当扰动量达50%时,此方法仍然有效,分析数值结果,从而对一般非均匀介质中的波场性质有了一个定性了解,结果与一般非均匀介质中的声波局部理论基本一致.
- 弹性波动方程 /
- 摄动参数 /
- 积分方程 /
- 积分迭代
Abstract: In this paper, the medium parameters of the elastic wave equation in inhomogeneous medium are rewritten by introducing the referential variables and the perturbational variables, and the wave equation whose sources are the medium parameter perturbational term in homogeneous medtam is obtained By usingthe Green function theory, the integral equation of the perturbational parmeters is obtained. Then the displacement field in homogeneous medium is considered the resultof the first iteration, and the displacement fisld is solved by this integral equation.When the perturbations of medium paranteters are about 50 percent, this method cansolve the displacement ficld effectirely. From the analysis of the numerical results, the characteristics of wave field in inhomogeneous medium are obtained. The results conform with the local principles of wave, function in inhomogeneous medium.
- elastic wave equation /
- perturbational parameters /
- integral equation /
- integral iteration

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参考文献(7)

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