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Group velocity as an eigensensitivity problem

Group velocity as an eigensensitivity problem
Group velocity as an eigensensitivity problem
We present the problem of computing the dispersion relation in the generic form of
a parameter dependent generalized eigenvalue problem–the wavenumber plays the role of this
parameter. By carrying out first order perturbation analysis in the spirit of Rayleigh, we obtain
an exact expression for group velocity from this eigen-sensitivity. The connection of the eigensensitivity
relationship with the stationarity of the Rayleigh’s quotient is explored. Illustrative
examples to demonstrate the idea are presented for a specific waveguide problem involving two
elastically coupled beams. Two numerical examples are given.
group velocity, eigenvalue sensitivity, rayleigh’s quotient, elastic waveguides
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e

Bhaskar, Atul (2009) Group velocity as an eigensensitivity problem. Proceedings of the 7th EUROMECH Solid Mechanics Conference, Portugal.

Record type: Conference or Workshop Item (Paper)

Abstract

We present the problem of computing the dispersion relation in the generic form of
a parameter dependent generalized eigenvalue problem–the wavenumber plays the role of this
parameter. By carrying out first order perturbation analysis in the spirit of Rayleigh, we obtain
an exact expression for group velocity from this eigen-sensitivity. The connection of the eigensensitivity
relationship with the stationarity of the Rayleigh’s quotient is explored. Illustrative
examples to demonstrate the idea are presented for a specific waveguide problem involving two
elastically coupled beams. Two numerical examples are given.

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More information

Published date: September 2009
Venue - Dates: Proceedings of the 7th EUROMECH Solid Mechanics Conference, Portugal, 2009-09-01
Keywords: group velocity, eigenvalue sensitivity, rayleigh’s quotient, elastic waveguides

Identifiers

Local EPrints ID: 149701
URI: https://eprints.soton.ac.uk/id/eprint/149701
PURE UUID: 7bb17738-3eec-4c3a-acec-4f6751640590

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Date deposited: 04 May 2010 10:44
Last modified: 18 Jul 2017 19:25

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