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Diffraction of elastic waves by a rigid circular disc*

Published online by Cambridge University Press:  24 October 2008

A. K. Mal ,
D. D. Ang  and
L. Knopoff
A. K. Mal
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles.
D. D. Ang
Affiliation:
Department of Mathematics, University of Saigon, Vietnam.
L. Knopoff
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles.
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Abstract

The problem of the diffraction of axisymmetric harmonic elastic waves by a rigid circular disc is reduced to finding the solution of a pair of integral equations of the second kind suitable for iteration at low frequencies. Using the principle of contraction mapping, the rate of convergence of the iteration procedure is discussed and the error caused by stopping at any particular stage estimated. Detailed calculations are given for plane compressional waves at normal incidence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 237 - 247
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Ang, D. D. and Knopoff, L.Proc. Nat. Acad. Sci., U.S.A. 52 (1964), 201–207.CrossRefGoogle Scholar
(2)Ang, D. D. and Knopoff, L.Proc. Nat. Acad. Sci., U.S.A. 52 (1964), 1075–1081.CrossRefGoogle Scholar
(3)Jones, D. S.Theory of electromagnetism (Pergamon Press, 1964).Google Scholar
(4)Jones, D. S.Proc. Cambridge Philos. Soc. 61 (1965), 223–245.CrossRefGoogle Scholar
(5)Miklowitz, J.Appl. Mech. Rev. 13 (1960), 865–878.Google Scholar
(6)Sneddon, I. N.Fourier transforms (McGraw-Hill, 1951).Google Scholar