2013 Fiscal Year Final Research Report
Asymptotic analysis for wave propagation in elasticity and inverse problems
| Project/Area Number |
22540111
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Gunma University |
|---|
Principal Investigator |
TANUMA Kazumi 群馬大学, 理工学研究院, 准教授 (60217156)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
NAKAMURA Gen 韓国・仁荷大学, 北海道大学, 数学科, 理学研究科, 教授 (50118535)
|
|---|
| Research Collaborator |
CHI-SING Man アメリカ合衆国・ケンタッキー大学, 数学科, 教授
|
|---|
| Project Period (FY) |
2010-04-01 – 2014-03-31
|
| Keywords | 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 |
|---|
| Research Abstract |
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.
|
