Properties of wave propagator and reflectivity in linear viscoelastic media

Abstract

An asymptotic analysis is applied to the relaxation function of a homogeneous viscoelastic material in order to study the propagation of transient waves and their reflection at a discontinuity surface. The wave propagator and the reflectivity kernel are derived for the one-dimensional problem in the form of a time expansion and are expressed in terms of hypergeometric functions. The decay of the wave front and the growth or decrease of the transient amplitude near the wave front are shown to be consequences of the relaxation properties. Also the behaviour of the non-instantaneous part of the reflectivity turns out to be connected with the thermodynamic restrictions on the relaxation function. The asymptotic approach is tested through a comparison with Maxwell's viscoelastic model.