Propagation of finite amplitude waves in elastic solids

Abstract

This thesis is devoted to consideration of finite amplitude waves propagating into an elastic half-space in a direction normal to the boundary. Excitation is by means of strains applied at the boundary as step functions of time. The solutions obtained are combinations of centered simple waves and shock waves. Longitudinal waves may appear alone but waves with transverse displacement components are always accompanied by longitudinal waves. The foregoing solutions are discussed in general and are illustrated by an example problem involving a special nonlinear, compressible, hyperelastic material. A perturbation method, based on the use of characteristic coordinates, which facilitates approximate solution of the problem for arbitrarily prescribed strain boundary conditions is described.