Elastic wave scattering by a circular crack

Abstract

The scattering of waves by a circular crack in an elastic medium is solved by a direct integral equation method. The solution method is based on expansion of stresses and displacements on the crack surface in terms of trigonometric functions and orthogonal polynomials. The expansion coefficients are related through an infinite matrix, and by contour integration the matrix elements are expressed in terms of finite integrals. The scattered far field is expressed explicitly in terms of simple functions and the displacement expansion coefficients. The system of equations is solved numerically, and extensive results are given both in the form of maps of the scattered far field and as scattering cross sections. Neither the method nor the specific results are restricted by any assumptions of symmetry.