Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T13:43:40.141Z Has data issue: false hasContentIssue false
  • English
  • Français

The diffraction of long elastic waves by elliptic cylindrical cavities

Published online by Cambridge University Press:  17 February 2009

V. T. Buchwald  and
T. Tran Cong
T. Tran Cong
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The method of asymptotic matching introduced by Buchwald [I] is adapted to the case of the diffraction of plane longitudinal and shear waves by cylindrical cavities with elliptic cross-sections. It is assumed that the dimensions of the cross section are small compared with the wavelength of the incident waves. Asymptotic formulae for the scattered wave potentials are obtained.

The method is valid when the cavity reduces to a two-dimensional stress free crack whose length is small compared with the wavelength. Formulae for the scattered waves, and for the stress-concentrations at the crack tips are obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 1 , July 1984 , pp. 108 - 118
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Buchwald, V. T., “The diffraction of elastic waves by small cylindrical cavities”, J. Austral. Math. Soc. Ser. B 20 (1978), 495–507.CrossRefGoogle Scholar
[2]Datta, S. K., “Scattering of elastic waves”, in Mechanics today, Vol. 4 (ed. Nemat-Nasser, S.), (Pergarnon Press, New York, 1978), 149–208.CrossRefGoogle Scholar
[3]Gautesen, A. K., “On matched asymptotic expansions for two dimensional elastodynamic diffraction by cracks”, Wave Motion 1 (1979), 127–140.CrossRefGoogle Scholar
[4]Green, A. E. and Zerna, W., Theoretical elasticity (Clarendon Press, Oxford, 1954).Google Scholar
[5]Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity (translated by Radok, J. R. M.), (Noordhoff, Groningen, 1953).Google Scholar
[6]Viswanathan, K. and Chandra, J., “On the matched asymptotic solution of elastodynaniic problems: loading over a semi-infinite rectangular boundary”, Wave Motion 1 (1979), 201–213.CrossRefGoogle Scholar