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On the propagation, reflection, and transmission of transient cylindrical shear waves in nonhomogeneous four-parameter viscoelastic media

Published online by Cambridge University Press:  17 April 2009

T. Bryant Moodie
T. Bryant Moodie
Affiliation:
Department of Mathematics, University of Dundee, Dundee, Scotland.
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Abstract

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The purpose of this paper is to study the propagation of cylindrical shear waves in nonhomogeneous four-parameter viscoelastic plates of arbitrary thickness. The plates have a transverse cylindrical hole and their material properties are functions of the radial distance from the center of this opening. They are initially unstressed and at rest. A suddenly rising shearing traction is applied uniformly over the boundary of the opening and parallel to the faces of the plates and thereafter steadily maintained; they are otherwise free from loading. We consider both the case of a finite plate with a stress-free cylindrical outer boundary, and an infinite plate composed of two media in welded contact along a cylindrical surface symmetrical with respect to the center of the opening. We find that a reflected pulse is produced at the outer boundary of the finite plate while reflected and transmitted pulses are produced at the interface in the infinite bi-viscoelastic plate. Ray techniques are used throughout, and formal asymptotic wavefront expansions of the solution functions are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 397 - 411
Copyright
Copyright © Australian Mathematical Society 1973

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