Similarity Analysis of the Elastic Wave Motion in a Dissipative Solid under aGlobal Relaxation Law

摘要

A similarity analysis is carried out on the elastic wave motion in a dissipativesolid under a global relaxation law. The solid is taken to be arbitrarily inhomogeneous and anisotropic. Global relaxation laws consisting of the combination of a frictional-force and a viscosity type are assumed to apply to the inertia and the compliance properties of the solid, i.e., the time derivatives in the first-order coupled wave equations are replaced by a relaxation operator with a constant coefficient. It is shown how in such a dissipative solid the elastic wave motion generated by arbitrary force type or deformation-rate type source distributions with bounded support is related to the wave motion in the lossless counterpart of the configuration. The similarity relation is based upon the Schouten-Van der Pol theorem in the theory of the one-sided Laplace transformation. As such, the similarity analysis generalizes earlier results obtained by Chao and Achenbach. (Copyright (c) 1993 American Sociey of Mechanical Engineers.)