Reflection of Plane Viscoelastic Waves from Plane Boundaries

Abstract

The reflection of time-harmonic plane dilatational or shear waves from the rigid or stressfree boundary of an “arbitrary” linearly viscoelastic half-space is studied. Properties of general plane waves—i.e., plane waves whose amplitudes vary across their wavefronts—are used to determine the reflected dilatational and shear waves. In general, the reflected waves are general plane waves and there is a phase shift at the boundary. When certain specified conditions prevail, the reflected waves are attenuated only in their direction of propagation. Necessary and sufficient conditions on the material properties are derived for the existence of surface waves. It is shown that no surface waves can exist for certain viscoelastic materials. In general, surface waves are possible only for discrete incidence angles. However, for a special class of viscoelastic materials, which we call elasticlike, reflected surface waves may exist for a range of incidence angles greater than a specific critical angle. For the elasticlike materials, the phase shift at the boundary is the same as in the analogous elastic problem. In general, the phase velocities and reflected angles are functions of the incidence angle, the frequency, and material properties.