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The attenuation of a Rayleigh wave in a half-space by a surface impedance

Published online by Cambridge University Press:  24 October 2008

R. D. Gregory
R. D. Gregory
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

A time harmonic Rayleigh wave, propagating in an elastic half-space y ≥ 0, is incident on a certain impedance boundary condition on y = 0, x > 0. The resulting field consists of a reflected surface wave, scattered body waves, and a transmitted surface wave appropriate to the new boundary conditions. The elastic potentials are found exactly by Fourier transform and the Wiener-Hopf technique in the case of a slightly dissipative medium. The ψ potential is found to have a logarithmic singularity at (0,0), but the φ potential though singular is bounded there. Analytic forms are given for the amplitudes of the reflected and transmitted surface waves, and for the scattered field. The reflexion coefficient is found to have a simple form for small impedances. A uniqueness theorem, based on energy considerations, is proved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 811 - 827
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

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