Axisymmetric Scattering of a Plane Longitudinal Wave by a Circular Crack in a Transversely Isotropic Solid

[+] Author and Article Information
T. Kundu

Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ 85721

A. Boström

Division of Mechanics, Chalmers University of Technology, S-412 96 Göteborg, Sweden

J. Appl. Mech 58(3), 695-702 (Sep 01, 1991) (8 pages) doi:10.1115/1.2897250 History: Received October 11, 1989; Revised June 05, 1990; Online March 31, 2008


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 perpendicular 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.

Copyright © 1991 by The American Society of Mechanical Engineers
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