Characteristics of group velocities of backward waves in a hollow cylinder

Cui, H.; Lin, W.; Zhang, H.; Wang, X.; Trevelyan, J.

doi:10.1121/1.4872297

Characteristics of group velocities of backward waves in a hollow cylinder

Cui, H.; Lin, W.; Zhang, H.; Wang, X.; Trevelyan, J.

Authors

H. Cui

W. Lin

H. Zhang

X. Wang

Jonathan Trevelyan jon.trevelyan@durham.ac.uk
Emeritus Professor

Abstract

It is known that modes in axially uniform waveguides exhibit backward-propagation characteristics for which group and phase velocities have opposite signs. For elastic plates, group velocities of backward Lamb waves depend only on Poisson's ratio. This paper explores ways to achieve a large group velocity of a backward mode in hollow cylinders by changing the outer to inner radius ratio, in order that such a mode with strong backward-propagation characteristics may be used in acoustic logging tools. Dispersion spectra of guided waves in hollow cylinders of varying radii are numerically simulated to explore the existence of backward modes and to choose the clearly visible backward modes with high group velocities. Analyses of group velocity characteristics show that only a small number of low order backward modes are suitable for practical use, and the radius ratio to reach the highest group velocity corresponds to the accidental degeneracy of neighboring pure transverse and compressional modes at the wavenumber k = 0. It is also shown that large group velocities of backward waves are achievable in hollow cylinders made of commonly encountered materials, which may bring cost benefits when using acoustic devices which take advantage of backward-propagation effects.

Citation

Cui, H., Lin, W., Zhang, H., Wang, X., & Trevelyan, J. (2014). Characteristics of group velocities of backward waves in a hollow cylinder. The Journal of the Acoustical Society of America, 135(6), 3398-3408. https://doi.org/10.1121/1.4872297

Journal Article Type	Article
Publication Date	Jun 1, 2014
Deposit Date	Nov 21, 2014
Publicly Available Date	Nov 24, 2014
Journal	The Journal of the Acoustical Society of America
Print ISSN	0001-4966
Publisher	Acoustical Society of America
Peer Reviewed	Peer Reviewed
Volume	135
Issue	6
Pages	3398-3408
DOI	https://doi.org/10.1121/1.4872297
Public URL	https://durham-repository.worktribe.com/output/1417237

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© 2014 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.
The following article appeared in Cui, Hanyin, Lin, Weijun, Zhang, Hailan, Wang, Xiuming and Trevelyan, Jon (2014) 'Characteristics of group velocities of backward waves in a hollow cylinder.', Journal of the Acoustical Society of America, 135 (6), 3398-3408 and may be found at http://dx.doi.org/10.1121/1.4872297.