On the inverse problem of the scattering of elastic waves by a thin foreign inclusion
type: Item
instance of: scholarly article
title: On the inverse problem of the scattering of elastic waves by a thin foreign inclusion
zbMATH Open document ID: 0622.73030
DOI: 10.1016/0021-8928(86)90111-5
author: V. F. Emets'
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: The problem of the remote determination of the shape of an isolated scatterer is considered using longitudinal elastic waves. It is assumed that the scatterer is a thin elastic solid of revolution situated in an elastic space under conditions of rigid contact and that Poisson's ratios of the medium and the scatterer are the same. The use of multifrequency wave information is a special feature of the solution of the problem. The problems of the uniqueness and stability of the solution obtained are also studied. We mean by the inverse scattering problem the problem of determining the form of the scattering region by analyzing the scattered field. The problem, as a rule, is one of a number of ill-posed problems of mathematical physics. The present paper uses the method given by the author, ibid. 48(1985), 89-92 (1984; Zbl 0566.73026) to solve the problem of determining the form of a thin elastic solid of revolution using the experimentally known scattering amplitude of longitudinal displacement waves specified on a discrete set of the sounding frequencies in a fixed direction in space. It is assumed here that Poisson's ratios of the medium and the solid in question are the same, and the solid is in rigid contact with the elastic medium.
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 35R25
zbMATH DE Number: 4009913
zbMATH Keywords: isolated scatterer
zbMATH Keywords: longitudinal elastic waves
zbMATH Keywords: thin elastic solid of revolution
zbMATH Keywords: rigid contact
zbMATH Keywords: Poisson's ratios
zbMATH Keywords: uniqueness
zbMATH Keywords: stability of the solution
zbMATH Keywords: ill-posed problems
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90111-5
OpenAlex ID: W2017635159
cites work: Q3965502
cites work: The inverse problem for convex bodies
cites work: Q5723698
cites work: Q5787627
cites work: Q3933322
description: scientific article; zbMATH DE number 4009913