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Wave propagation in inhomogeneous elastic media

DEPARTMENT OF MATHEMATICS UNIVERSITY OF STRATHCLYDE, GEORGE STREET GLASGOW C 1, Scotland

Abstract

The propagation of waves in an inhomogeneous elastic solid whose elastic parameters depend on one space coordinate only is considered. The stress and displacement components are assumed to depend on this same space coordinate and time alone. It is shown that the wave equation, with variable wave speed, is the basic equation governing the propagation of shear waves in spherical or cylindrical coordinates as well as the propagation of longitudinal waves in a rod. The values of the elastic parameters which permit a particular simple solution are determined and some problems are then discussed for these solids.

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