Development of representation of elastic waves and investigation of their fundamental properties

弹性波表示的发展及其基本特性的研究

• 批准号: 21540161
• 负责人: SOGA Hideo
• 金额: $ 2.58万
• 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: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540161/
• 关键词: 関数方程式; 弾性方程式; 偏微分方程式; 逆問題; 散乱波; 弾性波動方程式; 散乱問題; 複素積分

The purpose in this research is the following : (1) to develop a new representation of elastic waves and to apply this to inverse problems;(2) to investigate fundamental properties of elastic waves connected with the inverse problems.The above (1) is an attempt to develop a primitive idea obtained previously into a detailed form. Although we have encountered an unexpected serious difficulty in this attempt, we succeed finally in proving the conjectured conclusion, and moreover make relation clear between the obtained representation and the known ones. Also we obtain an algorithm for an inverse problem to measure pre-stress from data of surface waves (Rayleigh waves) expressed by the representation. This is based on a formula which shows how the pre-stress depends on the velocity of the Rayleigh wave.Concerning the above (2), we get new pieces of knowledge about the energy of waves. The one is verification that the energy propagates essentially along the characteristics. The other is precise estimation for influence of the dissipative terms to the energy decay. We show also the representation in (1) is useful to prove the Huygens principle for more extensive classes than previously known. Further, we have tried to prove the unique continuation property for the general elastic equation, as was planned, and get an idea for the proof. However, we do not accomplish this proof expected first.

本研究的目的是：（1）发展弹性波的一种新表示法，并将其应用于反问题;（2）研究与反问题有关的弹性波的基本性质。虽然我们在这一尝试中遇到了意想不到的严重困难，但我们最终成功地证明了所得到的结论，而且使所得到的表示与已知的表示之间的关系变得清楚。此外，我们得到了一个反问题的算法来测量预应力从数据的面波（瑞利波）表示。这是基于一个公式，该公式表明预应力如何取决于瑞利波的速度。关于上述（2），我们得到了关于波的能量的新知识。一个是验证能量基本上沿着特性传播。二是精确估计耗散项对能量衰减的影响。我们还表明，在（1）中的表示是有用的证明惠更斯原理更广泛的类比以前已知的。此外，我们已经尝试证明的唯一连续性的一般弹性方程，如计划，并得到一个想法的证明。然而，我们并没有首先完成预期的证明。

项目成果

Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

• DOI: 10.1177/1081286512438882
• 发表时间: 2013-05
• 期刊: Mathematics and Mechanics of Solids
• 影响因子: 2.6
• 作者: Kazumi Tanuma;C. Man;Wenwen Du

Weighted energy estimates for wave equations in exterior domains

外部域波动方程的加权能量估计

• 期刊: orum Math (掲載決定)
• 作者: M. Kawashita;H. Sugimoto
• 通讯作者: H. Sugimoto

Cauchy積分を使った弾性波の漸近展開

使用柯西积分的弹性波渐近展开

• 发表时间: 2011
• 作者: 井上学;石村直之;中村正彰;M. Kawashita and K. Suzuki;K. Saito;Asao Arai;曽我日出夫
• 通讯作者: 曽我日出夫

Local energy decay for wave equations in exterior domains with regular or fast decaying dissipations

具有规则或快速衰减耗散的外部域中波动方程的局部能量衰减

• 发表时间: 2011
• 期刊: SUT Journal of Mathematics
• 作者: 畑沙緒里;杉江実郎;杉江実郎;Miwako Mishima;Ryo Ikehata;Hiroyasu Mizuguchi;N. NAWATA and Y. WATATANI;Masakazu Jimbo;杉江実郎;M. Kawashita and K. Suzuki
• 通讯作者: M. Kawashita and K. Suzuki