A Unified Approach to Cylindrical and Spherical Elastic Waves by Method of Characteristics

Abstract

A set of generalized equations is presented which governs the propagation of plane, cylindrical, and spherical dilatation waves in elastic media. The corresponding characteristic equations are then derived, including the propagation of abrupt changes (discontinuous wave fronts). Procedures of numerical integration along the characteristic directions are established and carried out for several examples on a digital computer. The solutions of four of the specific examples calculated show excellent agreement with existing solutions by other methods.