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Analytic solutions of the radiation modes problem and the active control of sound power

Analytic solutions of the radiation modes problem and the active control of sound power
Analytic solutions of the radiation modes problem and the active control of sound power
This paper explores the common mathematical foundation of two different problems: the first one arises in electrical engineering for the detection and the spectral estimation of signals in noise and the second one appears in acoustics for the calculation of the acoustic radiation modes of rectangular structures. Although apparently unrelated, it is found that both applications draw on the so-called concentration problem: of determining which functions that are band-limited in one domain have maximal energy concentration within a region of the transform domain. The analytic solutions to problems of this form are seen to involve prolate spheroidal wave functions. In particular, exact expressions are given for the radiation efficiencies and shapes of the radiation modes of a baffled beam as well as their asymptotics. It is shown that a generalization of the concentration problem to the two-dimensional case provides analytic solutions that solve with a good accuracy, although approximately, the radiation problem. The properties of these special functions provide a rigorous basis of understanding some previously observed features of these applications, namely the grouping property of the radiation modes of a baffled panel and the physical limitations for the active control of sound from a panel.
structural acoustics, concentration problem, radiation modes, active noise control
2157-2160
Maury, C.
abaad9e5-79ef-4544-bf4a-02b779e4aade
Elliott, S.J.
721dc55c-8c3e-4895-b9c4-82f62abd3567
Maury, C.
abaad9e5-79ef-4544-bf4a-02b779e4aade
Elliott, S.J.
721dc55c-8c3e-4895-b9c4-82f62abd3567

Maury, C. and Elliott, S.J. (2004) Analytic solutions of the radiation modes problem and the active control of sound power. ICA2004 :The 18th International Congress on Acoustics, Kyoto, Japan. 04 - 09 Apr 2004. pp. 2157-2160 . (doi:10.1098/rspa.2004.1357).

Record type: Conference or Workshop Item (Paper)

Abstract

This paper explores the common mathematical foundation of two different problems: the first one arises in electrical engineering for the detection and the spectral estimation of signals in noise and the second one appears in acoustics for the calculation of the acoustic radiation modes of rectangular structures. Although apparently unrelated, it is found that both applications draw on the so-called concentration problem: of determining which functions that are band-limited in one domain have maximal energy concentration within a region of the transform domain. The analytic solutions to problems of this form are seen to involve prolate spheroidal wave functions. In particular, exact expressions are given for the radiation efficiencies and shapes of the radiation modes of a baffled beam as well as their asymptotics. It is shown that a generalization of the concentration problem to the two-dimensional case provides analytic solutions that solve with a good accuracy, although approximately, the radiation problem. The properties of these special functions provide a rigorous basis of understanding some previously observed features of these applications, namely the grouping property of the radiation modes of a baffled panel and the physical limitations for the active control of sound from a panel.

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More information

Published date: 2004
Venue - Dates: ICA2004 :The 18th International Congress on Acoustics, Kyoto, Japan, 2004-04-04 - 2004-04-09
Keywords: structural acoustics, concentration problem, radiation modes, active noise control
Organisations: Signal Processing & Control Group

Identifiers

Local EPrints ID: 11014
URI: http://eprints.soton.ac.uk/id/eprint/11014
PURE UUID: 4fa83375-f61d-4cd2-aa25-c3000df42e72

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Date deposited: 01 Apr 2005
Last modified: 15 Mar 2024 05:01

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Contributors

Author: C. Maury
Author: S.J. Elliott

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