Abstract:
Considerable progress has been made in performing time-harmonic response computations for bodies surrounded by unbounded acoustic fluid and solid media. However, computational impracticality has hindered progress in transient response analysis, which has motivated the development of approximate approaches. A 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 in between. Here, first- and second-order DAAs are derived for a uniform, isotropic, elastic medium of either infinite or semi-infinite extent. Following boundary-element semidiscretization, either of these approximations provides a computational boundary for a finite-element model of a ground-shock-excited structure and, if desired, surrounding soil island. The derivations proceed from pertinent singly asymptotic approximations and employ the method of operator matching previously used for acoustic fluid domains. A simple problem with spherical symmetry is considered that illustrates the characteristics of the singly and doubly asymptotic approximations. [Work supported by the Defense Nuclear Agency.]