Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T10:53:22.785Z Has data issue: false hasContentIssue false

Low frequency scattering of elastic waves by a cavity using a matched asymptotic expansion method

Published online by Cambridge University Press:  17 February 2009

L. Bencheikh
Affiliation:
Institut de Chimie Industrielle,University de Sétif, Sétif. 19000, Algérie.
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.

This work deals with low-frequency asymptotic solutions using the method of matched asymptotic expansions. It is based on two papers by Buchwald [3] and Buchwald and Tran Cong [4] who studied the diffraction of elastic waves by a small circular cavity and a small elliptic cavity, respectively, in an otherwise unbounded domain. Here we clarify and systematize some aspects of their work and extend it to the diffraction of elastic waves by a small cylindrical cavity with a hypotrochoidal boundary. Results for the case of an incident P-wave are compared, in the special case of an elliptic boundary, with the results from the numerical solution of the boundary integral equation method.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Bencheikh, L., “Modified fundamental solutions for the scattering of elastic waves by a cavity”, Q. J. Mech. Appl. Math. Part 1 43 (1990) 5773.CrossRefGoogle Scholar
[2]Bencheikh, L., “Modified fundamental solutions for the scattering of elastic waves by a cavity: numerical results”, Int. J. Num. Meth. Eng. 36 (1993) 32833302.Google Scholar
[3]Buchwald, V. T., “The diffraction of elastic waves by small cylindrical cavities”, J. Austral. Math. Soc. Ser. B 20 (1978) 495507.Google Scholar
[4]Buchwald, V. T. and Cong, T. Tran, “The diffraction of long elastic waves by elliptical cylindrical cavities”, J. Austral. Math. Soc. Ser. B 26 (1984) 108118.Google Scholar
[5]Crighton, D. G. and Leppington, F. G., “Singular perturbation medhods in acoustics: diffraction by a plate of finite thickness”, Proc. Roy. Soc. Lond. Ser. A 335 (1973) 313339.Google Scholar
[6]Datta, S. K., “Scattering of elastic waves”, in Mechanics Today (ed. Nemat-Nasser, S.), Volume 4, (Pergamon Press, New York, 1978) 149208.CrossRefGoogle Scholar
[7]England, A. H., Complex variable methods in elasticity (Wiley-Interscience, 1971).Google Scholar
[8]Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity (Noordhoff, Groningen, The Netherlands, 1963).Google Scholar
[9]Sabina, F. J. and Willis, J. R., “Scattering of SH waves by a rough half-space of arbitrary slope”, Geophy. J. Roy. Astr. Soc. 42 (1975) 685703.CrossRefGoogle Scholar