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Waveguide modes in elastic rods

Waveguide modes in elastic rods
Waveguide modes in elastic rods
This paper is concerned with wave propagation in elastic rods of cross-sectional shapes that admit coupling between bending and torsional motions. Dispersion relations for progressive and evanescent waves are presented in closed form. The general case of triple coupling and the special case of double coupling are considered. The propagation characteristics are analytically presented in the limits of the long and the short waves. Waveguide modes in these limits are presented as asymptotic expansions. The polarization behaviour in various regimes of propagation is studied. Eigenvalue veering is observed for coupled modes. For the complete spectrum involving complex wavenumber, the problem of obtaining the dispersion relation and the propagation modes is cast as a standard eigenproblem. Illustrative examples are given.
elastic waves, dispersion, bending-torsion coupling, asymptotic analysis, eigenvalue veering
1364-5021
175-194
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e

Bhaskar, Atul (2003) Waveguide modes in elastic rods. Proceedings of the Royal Society A, 459 (2029), 175-194. (doi:10.1098/rspa.2002.1013).

Record type: Article

Abstract

This paper is concerned with wave propagation in elastic rods of cross-sectional shapes that admit coupling between bending and torsional motions. Dispersion relations for progressive and evanescent waves are presented in closed form. The general case of triple coupling and the special case of double coupling are considered. The propagation characteristics are analytically presented in the limits of the long and the short waves. Waveguide modes in these limits are presented as asymptotic expansions. The polarization behaviour in various regimes of propagation is studied. Eigenvalue veering is observed for coupled modes. For the complete spectrum involving complex wavenumber, the problem of obtaining the dispersion relation and the propagation modes is cast as a standard eigenproblem. Illustrative examples are given.

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More information

Published date: 2003
Keywords: elastic waves, dispersion, bending-torsion coupling, asymptotic analysis, eigenvalue veering

Identifiers

Local EPrints ID: 22230
URI: http://eprints.soton.ac.uk/id/eprint/22230
ISSN: 1364-5021
PURE UUID: 17176748-8018-4cfa-9809-15a8d711e3b8

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Date deposited: 17 Mar 2006
Last modified: 07 Jan 2022 22:11

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