Diffraction of a spherical elastic wave by a wedge: PMM vol. 40, no. 5, 1976, pp. 898–908

Abstract

A three-dimensional nonstationary problem of spherical elastic wave diffraction by a smooth solid wedge with arbitrary apex angle is considered. An exact solution in the form of a sum of two terms, the known acoustic solution and an additional part describing the influence of elasticity, and caused by the appearance of additional longitudinal and transverse diffraction waves, is obtained by the method of integral transforms with extraction of the singularities in the neighborhood of an edge. This latter term essentially distinguishes the elastic from the acoustic solution. The particular case of an incident wave with a jump in the stresses at the front is investigated in detail. The corresponding acoustic problem has been examined in [1–4], where the solution in elementary functions was first obtained in [2]. Only the solution for the plane wave diffraction problem [5] is known for a wedge in the elastic case. Solutions found earlier for plane diffraction problems by a smooth wedge [6] and a smooth half-plane [7], which agree with the solution of the corresponding acoustic problems, are not true because of neglecting the condition at the edge, which indeed resulted in nonintegrable stresses in the neighborhood of the edge.