Pulse Propagation in a Nonlinear Viscoelastic Rod of Finite Length

Abstract

The problem of impact on a, nonlinear viscoelastic rod of finite length is considered. It is shown that, in the high frequency or geometrical acoustics limit, the disturbance in the rod may be represented as the superposition of two modulated simple waves traveling in opposite directions which do not interact in the body of the material. Based on this result the impact and initial boundary value problems are reduced to finding the solution of a nonlinear difference equation, which is solved exactly. We examine the competing effects of amplitude dispersion, which may produce shocks, and dissipation and give conditions under which each dominates. The corresponding results for an inhomogeneous rod are also given.