The transition matrix for the scattering of elastic waves in a half‐space

Autor:	Wen-I Liao, Tsung-Jen Teng, Juin-Fu Chai, Chau-Shioung Yeh
Rok vydání:	2007
Předmět:	symbols.namesake Matrix (mathematics) Scattering Mathematical analysis General Engineering Plane wave symbols Basis function Boundary value problem Rayleigh scattering Half-space Orthogonal basis Mathematics
Zdroj:	Journal of the Chinese Institute of Engineers. 30:983-996
ISSN:	2158-7299 0253-3839
Popis:	In this paper, the transition matrix for elastic waves scattering from an alluvium on an elastic half‐space is developed. Betti's third identity is employed to establish orthogonality conditions among basis functions that are Lamb's singular wave functions. The total displacements and associated tractions for both the surrounding half‐space and alluvium are expanded in a Rayleigh series. After the boundary conditions are applied, the T‐matrix can be obtained. Explicit forms of the basis functions are derived for the two‐dimensional anti‐plane and in‐plane problems. The linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T‐matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T‐matrix is also symmetric. Some typical scattering cases induced by incident plane waves are illustrated for verification.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5c3ad61fdac0c359d853c2d5405fcd94 https://doi.org/10.1080/02533839.2007.9671326 Zobrazit plný text záznamu