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Longitudinal wave propagation in an infinite isotropic elastic plate with a penny-shaped crack

Published online by Cambridge University Press:  24 October 2008

H. S. Paul
H. S. Paul
Affiliation:
Department of Mathematics, Indian Institute of Technology, Madras, India
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Extract

The stress distribution, subject to a constant pressure over the entire surface of a penny-shaped crack is discussed by Sneddon(4). Recently, Robertson (3) has considered the diffraction of a plane longitudinal wave by a penny-shaped crack on a semi-infinite elastic solid. In the present analysis, the propagation of longitudinal wave in an infinite isotropic elastic plate with a penny-shaped crack in the middle has been investigated. The plane longitudinal wave is moving in the positive direction of z-azis and is impinging on the surface of the penny-shaped crack. The dual integral equation technique of Noble(l) is utilized to solve the mixed boundary-value problem. The analysis closely follows the method used in the author's previous paper (2). The vertical displacement is analysed numerically.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 439 - 442
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Noble, B.Proc. Cambridge Philos. Soc. 59 (1963), 351–362.CrossRefGoogle Scholar
(2)Paux, H. S.J. Acoust. Soc. Amer. 42 (1967), 412–416.Google Scholar
(3)Robertson, I. A.Proc. Cambridge Philos. Soc. 63 (1967), 229–238.CrossRefGoogle Scholar
(4)Sneddon, I. N.Fourier transforms (McGraw-Hill, 1951).Google Scholar