Analysis of special waves in elastic bodies

弹性体中的特殊波分析

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640151/
• 关键词: Elastic Waves; Wave Equations; Scattering Theory; Asymptotic Solutions; Reflection; Energy Decay; Mathematical Physics; Hyperbolic Equations; 弾性方程式; 表面波; 全反射; 逆問題; 双曲系方程式

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.

该研究项目与弹性波有关，主要目的最初是为了获得解决方案的混凝土表示，b）在边界附近研究波浪的散射，c）研究有关边界接近边界的逆问题，d）分析了总反应的波浪。让我们总结该项目中获得的结果。人们非常有望在分析弹性和弹性波的反问题的现象中有用。此外，我们还获得了波浪的另一种混凝土表示。b），我们已经表明，从很久以来以来，雷利波（Rayleigh Wave）就很早就表现出来，并且可以在lax-phillips散射理论中提取：我们已经为雷尔波（Rayleigh Wave）提出了对雷尔（Rayleigh Wave）的表述，这对雷利（Rayle）有用，这对逆向问题有用。此外，我们已经研究了表达无限行为的这一波的衰减。我们为近似解决方案获得了有限元的新数值方法。这些对于解决反问题似乎非常有用，但是我们不能具体解决某些反问题。