Doubly asymptotic approximations for transient elastodynamics

doubly asymptotic approximation (DAA) is an approximate temporal impedance relation at the boundary of a continuous medium : it approaches exactness at both early and late times, effecting a smooth transition between. Here, first- and second-order DAAs are derived for a uniform, isotropic, elastic medium of either infinite or semi-infinite extent. The derivations proceed from pertinent singly asymptotic approximations and employ the method of operator matching previously used for acoustic domains. A simple problem with spherical symmetry is considered that illustrates the characteristics of the singly and doubly asymptotic approximations. IT) 1997 Elsevier Science Ltd. All rights reserved.