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Doubly asymptotic approximations for transient elastodynamics. (English) Zbl 0944.74570
Summary: 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 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.
MSC:
74J10Bulk waves (solid mechanics)
74S30Other numerical methods in solid mechanics