Axisymmetric scattering of a plane longitudinal wave by a circular crack in a transversely isotropic solid

Tribikram Kundu, A. Bostroem

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendiculr to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.

Original languageEnglish (US)
Pages (from-to)695-702
Number of pages8
JournalJournal of Applied Mechanics, Transactions ASME
Volume58
Issue number3
StatePublished - Sep 1991

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longitudinal waves
cracks
Scattering
Cracks
Legendre functions
scattering
integral equations
Integral equations
surface cracks
Polynomials
elastic waves
Elastic waves
far fields
manipulators
boundary conditions
Boundary conditions
symmetry

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials

Cite this

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AB - The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendiculr to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.

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