Transmission of Plane Waves through Layered Linear Viscoelastic Media

The two-dimensional propagation of time-harmonic plane waves through a plane horizontally layered viscoelastic medium is discussed. The problem is formulated as the equivalent elastic plane-strain case with modified Lamé constants, which are complex and frequency dependent, replacing the usual elastic Lamé constants. Rather than use potentials, incident angles, etc., we formulate the problem directly in terms of stresses and displacements and solve it by using matrix methods. This approach is felt to be more direct and leads to some interesting conclusions. If the incident wave is not attenuated in the direction parallel to the layering, interface waves can be generated only if one of the layers is “pseudoelastic,” i.e., has at least one real wave speed. In this case, the interface waves are generated in the same manner as in the purely elastic case. Such a physical problem would exist, for example, if the incident waves were to travel through a semi-infinite elastic half-space before striking the plane viscoelastic layers. If the incident wave is attenuated in the direction parallel to the layering, interface waves can be generated at specific angles of incidence and specific combinations of material parameters.