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The forced two dimensional oscillations of a rigid strip in smooth contact with a semi-infinite elastic solid

Published online by Cambridge University Press:  24 October 2008

G. R. Wickham
G. R. Wickham
Affiliation:
University of Manchester
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Abstract

In this paper we investigate a time harmonic plane strain problem in a homogeneous isotropic semi-infinite elastic solid with mixed boundary conditions on its surface. The boundary is free from applied stress apart from on an infinite strip where the tangential components of stress are zero, and the normal component of displacement is a prescribed function. By reducing the mixed boundary value problem to the solution of a Fredholm integral equation of the second kind, an existence theorem is proved and a simple low frequency asymptotic formula relating the normal stress to the prescribed displacement is derived rigorously. The results are applied to the forced heaving and rocking motion of a rigid cylindrical body in smooth contact with an elastic half space. Some further applications to scattering problems are suggested.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 291 - 311
Copyright
Copyright © Cambridge Philosophical Society 1977

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