Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T20:38:48.487Z Has data issue: false hasContentIssue false
  • English
  • Français

On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs

Published online by Cambridge University Press:  08 July 2009

C. E. Athanasiadis ,
G. Pelekanos ,
V. Sevroglou  and
I. G. Stratis
C. E. Athanasiadis
Affiliation:
Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Zographou, Greece ([email protected])
G. Pelekanos
Affiliation:
Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, IL 62026, USA ([email protected])
V. Sevroglou
Affiliation:
Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece ([email protected])
I. G. Stratis
Affiliation:
Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Zographou, Greece ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and general scattering theorems and mixed scattering relations are presented. The direct scattering problem for a rigid circular disc is considered, and the exact Green function and the elastic far-field patterns of the radiating solution in the form of infinite series are obtained. Under the low-frequency assumption, approximations for the longitudinal and transverse far-field patterns of the scattered field are obtained, in addition to an asymptotic expansion for the corresponding scattering cross-section. A simple inversion scheme that locates the radius and the position of a rigid circular disc, which is based on a closed-form approximation of the scattered field at the location of the incident point source, is proposed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 719 - 741
Copyright
Copyright © Royal Society of Edinburgh 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)