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The active minimization of harmonic enclosed sound fields, part II: A computer simulation

The active minimization of harmonic enclosed sound fields, part II: A computer simulation
The active minimization of harmonic enclosed sound fields, part II: A computer simulation

This paper is Part II in a series of three papers on the active minimization of harmonic enclosed sound fields. In Part I it was shown that in order to achieve appreciable reductions in the total time averaged acoustic potential energy, Ep, in an enclosed sound field of high modal density then the primary and secondary sources must be separated by less than one half wavelength, even when a relatively large number of secondary sources are used. In this report the same theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the use of a computer model of a shallow rectangular enclosure it is demonstrated that whilst the reductions in Ep which can be achieved are still critically dependent on the source locations, the criteria governing the levels of reduction are somewhat different. In particular it is shown that for a lightly damped sound field of low modal density substantial reductions in Ep can be achieved by using a single secondary source placed greater than half a wavelength from the primary source, provided that the source is placed at a maximum of the primary sound field. The problems of applying this idealized form of active noise control are then discussed, and a more practical method is presented. This involves the sampling of the sound field at a number of discrete sensor locations, and then minimizing the sum of the squared pressures at these locations. Again by use of the computer model of a shallow rectangular enclosure, the effects of the number of sensors and of the locations of these sensors are investigated. It is demonstrated that when a single mode dominates the response near optimal reductions in Ep can be achieved by minimizing the pressure at a single sensor, provided the sensor is at a maximum of the primary sound field. When two or three modes dominate the response it is found that if only a limited number of sensors are available then minimizing the sum of the squared pressures in the corners of the enclosure gives the best reductions in Ep. The reasons for this behaviour are discussed.

0022-460X
15-33
Bullmore, A. J.
320a3079-679c-4ef0-97ab-7bb0c632e9ad
Nelson, P. A.
5c6f5cc9-ea52-4fe2-9edf-05d696b0c1a9
Curtis, A. R.D.
79ce7e69-6528-4453-ac93-9f80c0bfc340
Elliott, S. J.
721dc55c-8c3e-4895-b9c4-82f62abd3567
Bullmore, A. J.
320a3079-679c-4ef0-97ab-7bb0c632e9ad
Nelson, P. A.
5c6f5cc9-ea52-4fe2-9edf-05d696b0c1a9
Curtis, A. R.D.
79ce7e69-6528-4453-ac93-9f80c0bfc340
Elliott, S. J.
721dc55c-8c3e-4895-b9c4-82f62abd3567

Bullmore, A. J., Nelson, P. A., Curtis, A. R.D. and Elliott, S. J. (1987) The active minimization of harmonic enclosed sound fields, part II: A computer simulation. Journal of Sound and Vibration, 117 (1), 15-33. (doi:10.1016/0022-460X(87)90433-0).

Record type: Article

Abstract

This paper is Part II in a series of three papers on the active minimization of harmonic enclosed sound fields. In Part I it was shown that in order to achieve appreciable reductions in the total time averaged acoustic potential energy, Ep, in an enclosed sound field of high modal density then the primary and secondary sources must be separated by less than one half wavelength, even when a relatively large number of secondary sources are used. In this report the same theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the use of a computer model of a shallow rectangular enclosure it is demonstrated that whilst the reductions in Ep which can be achieved are still critically dependent on the source locations, the criteria governing the levels of reduction are somewhat different. In particular it is shown that for a lightly damped sound field of low modal density substantial reductions in Ep can be achieved by using a single secondary source placed greater than half a wavelength from the primary source, provided that the source is placed at a maximum of the primary sound field. The problems of applying this idealized form of active noise control are then discussed, and a more practical method is presented. This involves the sampling of the sound field at a number of discrete sensor locations, and then minimizing the sum of the squared pressures at these locations. Again by use of the computer model of a shallow rectangular enclosure, the effects of the number of sensors and of the locations of these sensors are investigated. It is demonstrated that when a single mode dominates the response near optimal reductions in Ep can be achieved by minimizing the pressure at a single sensor, provided the sensor is at a maximum of the primary sound field. When two or three modes dominate the response it is found that if only a limited number of sensors are available then minimizing the sum of the squared pressures in the corners of the enclosure gives the best reductions in Ep. The reasons for this behaviour are discussed.

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More information

Published date: 22 August 1987
Additional Information: Funding Information: S. J. Elliott and P. A. Nelson are supported by the Science and Engineering Research Council under the Special Replacement Scheme; the Department of Trade and Indrlstry research grant which supports A. R. D. Curtis and A. J. Bullmore also is gratefully acknowledged. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.

Identifiers

Local EPrints ID: 468577
URI: http://eprints.soton.ac.uk/id/eprint/468577
ISSN: 0022-460X
PURE UUID: d8ad3119-9f84-4fca-8749-4b90c1dfc082
ORCID for P. A. Nelson: ORCID iD orcid.org/0000-0002-9563-3235

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Date deposited: 18 Aug 2022 16:40
Last modified: 18 Mar 2024 02:31

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Contributors

Author: A. J. Bullmore
Author: P. A. Nelson ORCID iD
Author: A. R.D. Curtis
Author: S. J. Elliott

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