Analysis of special waves in elastic bodies

弹性体中的特殊波分析

基本信息

批准号：
10640151
负责人：
SOGA Hideo
金额：
$ 1.86万
依托单位：
Ibaraki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

This research project is concerned with elastic waves, and the main purposes set initially werea) to obtain concrete representations of the solutions,b) to study scattering of the waves near boundaries,c) to study inverse problems concerning the waves near boundaries,d) to analyze the waves in the case of the total reflection.We have accomplished these almost as was expected. Let us summarize the results obtained in this project.About a) and d) , we have got an asymptotic expansion of the wave reflected totally, which is one of the mainest results. This expansion is much expected to be useful in analyzing the phenomenon of the scattering and the inverse problems of the elastic waves. Furthermore, we have obtained also another kind of concrete representation of the waves.About b) , we have shown that the Rayleigh wave, which has been much interested since a long time ago, behaves individually and can be extracted in the Lax-Phillips scattering theory : We have made a formulation of that theory for the Rayleigh wave, which is useful for the inverse problems. Moreover, we have investigated precisely decay of this wave expressing the behavior at infinity.About c) , we have got a new methods of reconstruction of coefficients in differential equations applicable to the inverse problems. And we have obtained a new numerical method of finite elements for the approximate solutions. These seem to be very useful to solve the inverse problems, but we cannot finish solving concretely some of the inverse problems.

该研究项目涉及弹性波，最初设定的主要目的是：获得解决方案的具体表示，b）研究边界附近波的散射，c）研究边界附近波的反演问题，d）分析全反射情况下的波。我们几乎按照预期完成了这些工作。让我们总结一下这个项目中获得的结果。关于a)和d)，我们得到了全反射波的渐近展开，这是最重要的结果之一。人们普遍认为这种展开对于分析散射现象和弹性波的反演问题很有用。此外，我们还获得了波的另一种具体表示。关于 b)，我们已经证明了长期以来人们一直很感兴趣的瑞利波，它具有单独的行为，并且可以在 Lax-Phillips 散射中提取理论：我们已经为瑞利波制定了该理论的公式，这对于反演问题很有用。此外，我们还精确地研究了表达无穷远处行为的波的衰减。关于c)，我们得到了一种适用于反问题的微分方程系数重构的新方法。并得到了一种新的有限元数值方法的近似解。这些看起来对于解决逆问题很有用，但是有些逆问题我们还不能具体解决。