Skip Navigation


The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on September 15, 2005
The Quarterly Journal of Mechanics and Applied Mathematics 2005 58(3):419-438; doi:10.1093/qjmam/hbi019
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
58/3/419    most recent
hbi019v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (2)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Adamou, A. T. I.
Right arrow Articles by Craster, R. V.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Q. Jl Mech. Appl. Math, Vol. 58. No. 3 © The Author 2005. Published by Oxford University Press 2005; all rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

Acoustic quasi-modes in slowly varying cylindrical tubes

A. T. I. Adamou**, D. Gridin and R. V. Craster

( Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ )

** alexander.adamou{at}imperial.ac.uk

Guided wave propagation in slowly varying elastic bars is of increasing importance in the non-destructive evaluation of structures. This paper develops an asymptotic theory for the simpler case of an acoustic tube by extending the quasi-mode theory developed for two-dimensional geometries by Gridin and Craster to a three-dimensional guide of constant radius and slowly varying orientation. Quasi-modes are a generalization of the normal modes of a straight guide to the weakly curved case. Their properties depend on three lengthscales: the wavelength, the guide radius, and the length over which the guide's orientation typically varies. Different asymptotic regimes are encountered when the relative sizes of these lengthscales change. Asymptotic expressions for the quasi-modes are derived for two regimes in which the wavelength and guide radius are of similar size. The first regime holds when the wavelength is small compared to the scale of variation or, equivalently, the frequency is far from the cutoff frequency. The second applies when the wavelength is comparable to the scale of variation, or the frequency is close to the cutoff. A numerical scheme to solve the governing equations directly, which does not depend on the various lengthscales, is also developed to demonstrate the accuracy of the asymptotic expressions.

Received 7 December 2004. Revise 29 March 2005.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.