Propagation of elastic waves through media with thin crack-like inclusions
type: Item
instance of: scholarly article
title: Propagation of elastic waves through media with thin crack-like inclusions
zbMATH Open document ID: 0616.73038
DOI: 10.1016/0021-8928(86)90112-7
author: S. K. Kanaun
author: V. Levin
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: Wave propagation in elastic homogeneous media containing a random number of thin inclusions is studied. The material of the inclusions is assumed to be elastic or viscoelastic and appreciably softer than the medium surrounding them. Only the principal terms of the expansion of elastic fields in terms of the small parameters of the problem are considered, namely, the ratio of the characteristic linear dimensions of a typical inclusion and the ratio of the characteristic moduli of elasticity of the inclusion and the medium. This makes it possible to replace every inclusion by an equivalent model. The model problem of long-wave scattering by a single thin ellipsoidal inclusion is solved explicitly, and the solution is then used to study a medium containing a random number of thin defects. The effective-field method which takes into account multiple scattering of waves is used to obtain the averaged equation of motion of such a medium (the effective wave operator) in the long-wave approximation. The operator describes the wave propagation in a homogeneous medium with dispersion and attenuation. The velocities of propagation and the attenuation coefficients of various types of elastic waves propagating through materials with randomly oriented inclusions or cracks, and with a system of parallel cracks, are found.
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74R05
zbMATH DE Number: 3999399
zbMATH Keywords: elastic homogeneous media
zbMATH Keywords: random number of thin inclusions
zbMATH Keywords: viscoelastic
zbMATH Keywords: long-wave scattering
zbMATH Keywords: random number of thin defects
zbMATH Keywords: multiple scattering
zbMATH Keywords: averaged equation of motion
zbMATH Keywords: attenuation
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90112-7
OpenAlex ID: W1973044448
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description: scientific article; zbMATH DE number 3999399