Elastic wave scattering by a circular crack in a transversely isotropic solid

Tribikram Kundu, A. Boström

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.

Original languageEnglish (US)
Pages (from-to)285-300
Number of pages16
JournalWave Motion
Volume15
Issue number3
DOIs
StatePublished - 1992

Fingerprint

crack opening displacement
wave scattering
elastic waves
elastic scattering
cracks
integral equations
Legendre functions
far fields
manipulators
plane waves
symmetry
scattering

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics

Cite this

Elastic wave scattering by a circular crack in a transversely isotropic solid. / Kundu, Tribikram; Boström, A.

In: Wave Motion, Vol. 15, No. 3, 1992, p. 285-300.

Research output: Contribution to journalArticle

@article{5a01f08b8b024ead91034f8223220cf5,
title = "Elastic wave scattering by a circular crack in a transversely isotropic solid",
abstract = "The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.",
author = "Tribikram Kundu and A. Bostr{\"o}m",
year = "1992",
doi = "10.1016/0165-2125(92)90012-Q",
language = "English (US)",
volume = "15",
pages = "285--300",
journal = "Wave Motion",
issn = "0165-2125",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Elastic wave scattering by a circular crack in a transversely isotropic solid

AU - Kundu, Tribikram

AU - Boström, A.

PY - 1992

Y1 - 1992

N2 - The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.

AB - The scattering of arbitrary elastic waves by a circular crack in a tranversely isotropic solid is investigated. The symmetry axis of the solid and the normal to the crack are parallel. The problem is first divided into a symmetric and an antisymmetric part with respect to the plane of the crack. A Fourier-Hankel representation for the scattered field is then assumed and some manipulations using the conditions in the plane of the crack lead to an integral equation for the normal crack opening displacement for the symmetric part and two coupled integral equations for the tangential components of the crack opening displacement for the antisymmetric part. The crack opening displacements are expanded in series of Legendre functions which fulfil the correct edge conditions and the integral equations are projected on the same set of Legendre functions. The far field is calculated with the stationary phase method. Numerical results are given for crack opening displacements for incident quasi P and SV plane waves and compared with corresponding results for an isotropic solid.

UR - http://www.scopus.com/inward/record.url?scp=38249014715&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249014715&partnerID=8YFLogxK

U2 - 10.1016/0165-2125(92)90012-Q

DO - 10.1016/0165-2125(92)90012-Q

M3 - Article

AN - SCOPUS:38249014715

VL - 15

SP - 285

EP - 300

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 3

ER -