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Diffraction of a plane longitudinal wave by a penny-shaped crack

Published online by Cambridge University Press:  24 October 2008

Ian A. Robertson
Ian A. Robertson
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
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Extract

Introduction. The distribution of stress produced in the interior of an infinite elastic solid when a constant pressure is applied over the entire surface of a penny-shaped crack has been solved by Sneddon(6), (7). The problem considered here is the closely allied one of a plane longitudinal wave, harmonic in time, moving in the positive direction of the z-axis and impinging on the surface of a penny-shaped crack. The analysis follows the methods adopted for dealing with an axisymmetrical vibrating punch acting on a semi-infinite elastic solid, Robertson (5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 229 - 238
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

(1)Barratt, P. J. and Collins, W. D.Proc. Cambridge Philos. Soc. 61 (1965), 969–981.CrossRefGoogle Scholar
(2)Erdélyi, A.Asymptotic expansions (Dover, 1956).Google Scholar
(3)Noble, B.Proc. Cambridge Philos. Soc. 59 (1963), 351–362.CrossRefGoogle Scholar
(4)Noble, B.The Wiener-Hopf technique (Pergamon Press, 1958).Google Scholar
(5)Robertson, I. A.Proc. Cambridge Philos. Soc.Google Scholar
(6)Sneddon, I. N.Fourier transforms (McGraw-Hill, 1951).Google Scholar
(7)Sneddon, I. N.Crack problems in the mathematical theory of elasticity (North Carolina State College, 1961).Google Scholar
(8)Weatherburn, C. E.Advanced vector analysis (Bell, 1944).Google Scholar
(9)Watson, G. N.Bessel functions (Cambridge, 1944).Google Scholar