On the Transmission of Plane Waves through Layered Linear Viscoelastic Media

Abstract

The propagation of two-dimensional time harmonic waves through a plane layered viscoelastic medium is considered in terms of the equivalent elastic plane strain problem with modified Lamé constants that are complex and frequency dependent. The problem is formulated directly in terms of stresses and displacements rather than potentials and is solved by matrix methods. If the incident wave is not attenuated in the direction parallel to the layering, as would occur if the incident wave were to travel through a semi-infinite elastic half-space before striking the viscoelastic layers, interface waves could be generated only if one of the layers is “pseudoelastic,” i.e., has at least one real wave speed. In this case, interface waves may be generated in the same manner as in the purely elastic case. If the incident wave is attenuated in this direction, however, interface waves could be generated for specific angles of incidence and material properties.