Reflection and Transmission of Oblique Plane Waves at a Plane Interface between Viscoelastic Media

Abstract

The solution is obtained for the reflection and transmission of time harmonic plane dilatational or shear waves at a plane interface between two linearly viscoelastic materials. Except in special cases, the reflected and transmitted waves are general plane waves, i.e., plane waves whose amplitudes vary across their wave-fronts. The angles of reflection and transmission depend on the incident angle in a more complicated way than in the limiting elastic case because the wave speeds of the reflected and transmitted waves are, in general, functions of the incident angle. Necessary and sufficient conditions for the existence of interface waves are obtained. It is found that no interface waves can exist for some materials. For another class of materials, interface waves exist for discrete angles of incidence. For still other materials, interface waves exist for all incident angles greater than some critical angle.