Analytic solutions of the radiation modes problem and the active control of sound power
Maury, C. and Elliott, S.J. (2004) Analytic solutions of the radiation modes problem and the active control of sound power. In, ICA2004 :The 18th International Congress on Acoustics, Kyoto, Japan, 04 - 09 Apr 2004. 4pp, 2157-2160.
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Description/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.
| Item Type: | Conference or Workshop Item (Paper) |
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| Related URLs: | |
| Keywords: | structural acoustics, concentration problem, radiation modes, active noise control |
| Subjects: | Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > Institute of Sound and Vibration Research > Signal Processing and Control |
| Item ID: | 11014 |
| Date Deposited: | 01 Apr 2005 |
| Last Modified: | 01 Jun 2011 03:44 |
| Contributors: | Maury, C. (Author) Elliott, S.J. (Author) |
| Date: | 2004 |
| Status: | Published |
| URI: | http://eprints.soton.ac.uk/id/eprint/11014 |
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