Asymptotic analysis for wave propagation in elasticity and inverse problems

弹性和反问题中波传播的渐近分析

• 批准号: 22540111
• 负责人: TANUMA Kazumi
• 金额: $ 2.75万
• 依托单位: Gunma University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540111/
• 关键词: 応用解析; 弾性波; 非等方弾性体; Rayleigh 波; 残留応力; 逆問題; Stroh formalism; surface impedance; 国際研究者交流; アメリカ合衆国; 弾性波動方程式; 分散と摂動; 弾性界面波; 弾性表面波; Stoneley 波; 分散; Rayleigh波; 直交異方性; fiber-reinforced composites; 摂動公式; 分散公式; 弾性波動; 位相速度

In this research project we obtain a high-frequency asymptotic formula for the velocity of elastic surface waves (Rayleigh waves) which propagate along the surface of an inhomogeneous, anisotropic elastic media. This formula expresses the frequency-dependence of the Rayleigh-wave velocity, i.e., the dispersion of Rayleigh waves, as caused by the inhomogeneity of the medium. We also give a formula for the first-order perturbation of the velocity of Rayleigh waves and give a formula for that of interfacial waves which propagate along the bonded interface between two dissimilar semi-infinite anisotropic elastic media, as caused by the anisotropy of the media. These results can be applied to the inverse problems in non-destructive evaluation, seismology, and materials science, i.e., the problem of determining the anisotropy and the inhomogeneity of elastic media with initial stresses from boundary measurement of velocities of the aforementioned elastic waves.

在本研究计划中，我们得到了一个高频渐近公式的弹性表面波（瑞利波）的速度，传播沿着表面的非均匀，各向异性弹性介质。该公式表示瑞利波速度的频率依赖性，即，由于介质的不均匀性引起的瑞利波的色散。本文还给出了瑞利波速度的一阶摄动公式，以及由各向异性引起的沿沿着两种不同的半无限各向异性弹性介质间粘结界面传播的界面波速度的一阶摄动公式。这些结果可应用于非破坏性评价、地震学和材料科学中的反问题，即，由上述弹性波速度的边界测量确定具有初始应力的弹性介质的各向异性和不均匀性的问题。

项目成果

Perturbation and dispersion of phase velocity of Rayleigh waves in prestressed anisotropic elastic media

预应力各向异性弹性介质中瑞利波相速度的摄动与色散

• 发表时间: 2010
• 作者: Ijioma;E.;Muntean;A. and Ogawa;T.;Kazumi Tanuma;緒方秀教,桂田祐史;T.Nakai;Syoiti Ninomiya;Kazumi Tanuma
• 通讯作者: Kazumi Tanuma

Perturbation and dispersion of Rayleigh waves in prestressed anisotropic elastic media

预应力各向异性弹性介质中瑞利波的摄动与色散

• 发表时间: 2010
• 作者: Kazumi Tanuma;Chi-Sing Man;Kazumi Tanuma;Kazumi Tanuma
• 通讯作者: Kazumi Tanuma

非等方弾性体におけるStoneley波速度の摂動

各向异性弹性体中斯通利波速的扰动

• 发表时间: 2013
• 作者: A.Kira;T.Ueno;T.Fujita;待田 芳徳;二宮祥一;田沼一実
• 通讯作者: 田沼一実

Dispersion of Rayleigh Waves in Vertically-Inhomogeneous Prestressed Elastic Media

垂直非均匀预应力弹性介质中瑞利波的色散

• DOI: 10.1093/imamat/hxt025
• 发表时间: 2013
• 期刊: IMA Journal of Applied Mathematics
• 影响因子: 1.2
• 作者: Kota Takeuchi;Akito Tsuboi;Chi-Sing Man,Gen Nakamura,Kazumi Tanuma and Shengzhang Wang
• 通讯作者: Chi-Sing Man,Gen Nakamura,Kazumi Tanuma and Shengzhang Wang

Perturbation of Rayleigh waves and interfacial waves in anisotropic elastic media

各向异性弹性介质中瑞利波和界面波的扰动

• 发表时间: 2013
• 作者: Kazumi Tanuma;Chi-Sing Man and Wenwen Du
• 通讯作者: Chi-Sing Man and Wenwen Du