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Periodic orbit theory in acoustics: spectral fluctuations in circular and annular waveguides

Periodic orbit theory in acoustics: spectral fluctuations in circular and annular waveguides
Periodic orbit theory in acoustics: spectral fluctuations in circular and annular waveguides
Formulas based on the theory of Weyl are widely used to obtain the average number of modes at or below a given frequency in acoustic and vibrational waveguides. These formulas are valid at asymptotically high frequencies; at finite frequencies they are subject to some error, due to fluctuations in the mode count, which depend on the shape of the waveguide. The periodic orbit theory of semiclassical physics is used to give estimates of the variance of these fluctuations and these results are compared with numerical estimates based on eigenvalues obtained by root-finding. The comparison is good but shows errors that can be related to the nature of the periodic orbit theory. Engineering formulas are provided that give an accurate approximation without significant computational cost. The results are valid for membranes, ducts, and thin plates with clamped and/or simply supported boundary conditions.
0001-4966
1865-1872
Wright, M.C.M.
b7209187-993d-4f18-8003-9f41aaf88abf
Ham, C.J.
f90c0361-c63b-4121-a464-243c2d124a0d
Wright, M.C.M.
b7209187-993d-4f18-8003-9f41aaf88abf
Ham, C.J.
f90c0361-c63b-4121-a464-243c2d124a0d

Wright, M.C.M. and Ham, C.J. (2007) Periodic orbit theory in acoustics: spectral fluctuations in circular and annular waveguides. Journal of the Acoustical Society of America, 121 (4), 1865-1872. (doi:10.1121/1.2709407).

Record type: Article

Abstract

Formulas based on the theory of Weyl are widely used to obtain the average number of modes at or below a given frequency in acoustic and vibrational waveguides. These formulas are valid at asymptotically high frequencies; at finite frequencies they are subject to some error, due to fluctuations in the mode count, which depend on the shape of the waveguide. The periodic orbit theory of semiclassical physics is used to give estimates of the variance of these fluctuations and these results are compared with numerical estimates based on eigenvalues obtained by root-finding. The comparison is good but shows errors that can be related to the nature of the periodic orbit theory. Engineering formulas are provided that give an accurate approximation without significant computational cost. The results are valid for membranes, ducts, and thin plates with clamped and/or simply supported boundary conditions.

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Published date: 2007

Identifiers

Local EPrints ID: 46276
URI: https://eprints.soton.ac.uk/id/eprint/46276
ISSN: 0001-4966
PURE UUID: 90d8cc31-8185-4ce8-90d5-91406acece41

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Date deposited: 12 Jun 2007
Last modified: 13 Mar 2019 21:03

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