Uniaxial pulse propagation in a viscoelastic medium governed by a Boltzmann superposition integral

Abstract

The problem of pulse propagation through a linear viscoelastic medium is formulated by using the Boltzmann superposition integral. The relaxation times and coefficients which describe the modulus of a real material are therefore used directly in the formulation. The basic equation governing the wave motion is a partial integro-differential equation. The resulting initial value problem is solved via Laplace transforms and the asymptotic behavior of the solution is discussed. Pulse shapes for a real material (monodispersive polystrene) are calculated by using the numerical procedure of Dubner and Abate to evaluate the inverse laplace transforms.