Diffraction of Steady Elastic Waves by Surfaces of Arbitrary Shape

Abstract

The diffraction of steady-state elastic waves from arbitrarily shaped inclusions in an infinite medium is described by means of simultaneous singular integral equations expressed in terms of a set of displacement potentials. In contrast to some other formulations, this procedure permits the incorporation of the boundary conditions without approximation and the possibility of discontinuities in the surface of the diffracting object, such as cusps and corners, in the solution of the problem. The solution of the integral equations yields the potential functions at the interface which, in turn, are employed to derive the field potentials by surface integration. The formulation is presented for the two-dimensional case for an inclusion fixed in space which may be a void, a rigid body, or another elastic medium. The equations are solved by means of finite-difference approximations to the contour integrals. The resulting scattered field was found to be in excellent agreement with that obtained from a series solution of the diffraction of a plane compression wave from a rigid circular cylinder. Solutions of other two-dimensional configurations of interest involving rigid bodies are also presented. The corresponding acoustic cases, which have previously been examined, can be analyzed in an identical manner and numerical values established with a substantially lower level of computational effort.