The University of Southampton
University of Southampton Institutional Repository

A wavenumber approach to analysing the active control of plane waves with arrays of secondary sources

A wavenumber approach to analysing the active control of plane waves with arrays of secondary sources
A wavenumber approach to analysing the active control of plane waves with arrays of secondary sources
The active control of an incident sound field with an array of secondary sources is a fundamental problem in active control. In this paper the optimal performance of an infinite array of secondary sources in controlling a plane incident sound wave is first considered in free space. An analytic solution for normal incidence plane waves is presented, indicating a clear cut-off frequency for good performance, when the separation distance between the uniformly-spaced sources is equal to a wavelength. The extent of the near field pressure close to the source array is also quantified, since this determines the positions of the error microphones in a practical arrangement. The theory is also extended to oblique incident waves. This result is then compared with numerical simulations of controlling the sound power radiated through an open aperture in a rigid wall, subject to an incident plane wave, using an array of secondary sources in the aperture. In this case the diffraction through the aperture becomes important when its size is compatible with the acoustic wavelength, in which case only a few sources are necessary for good control. When the size of the aperture is large compared to the wavelength, and diffraction is less important but more secondary sources need to be used for good control, the results then become similar to those for the free field problem with an infinite source array.
0022-460X
405-419
Elliott, Stephen J.
721dc55c-8c3e-4895-b9c4-82f62abd3567
Cheer, Jordan
8e452f50-4c7d-4d4e-913a-34015e99b9dc
Lam, Bhan
aafb1b4c-ce14-4909-97f4-9775b11f4348
Shi, Chuang
d52fbe2b-3c97-4678-ab8e-230e2dc500e7
Gan, Woon-Seng
1936c59c-0552-498c-86a4-20bb81bb561a
Elliott, Stephen J.
721dc55c-8c3e-4895-b9c4-82f62abd3567
Cheer, Jordan
8e452f50-4c7d-4d4e-913a-34015e99b9dc
Lam, Bhan
aafb1b4c-ce14-4909-97f4-9775b11f4348
Shi, Chuang
d52fbe2b-3c97-4678-ab8e-230e2dc500e7
Gan, Woon-Seng
1936c59c-0552-498c-86a4-20bb81bb561a

Elliott, Stephen J., Cheer, Jordan, Lam, Bhan, Shi, Chuang and Gan, Woon-Seng (2018) A wavenumber approach to analysing the active control of plane waves with arrays of secondary sources. Journal of Sound and Vibration, 419, 405-419. (doi:10.1016/j.jsv.2018.01.028).

Record type: Article

Abstract

The active control of an incident sound field with an array of secondary sources is a fundamental problem in active control. In this paper the optimal performance of an infinite array of secondary sources in controlling a plane incident sound wave is first considered in free space. An analytic solution for normal incidence plane waves is presented, indicating a clear cut-off frequency for good performance, when the separation distance between the uniformly-spaced sources is equal to a wavelength. The extent of the near field pressure close to the source array is also quantified, since this determines the positions of the error microphones in a practical arrangement. The theory is also extended to oblique incident waves. This result is then compared with numerical simulations of controlling the sound power radiated through an open aperture in a rigid wall, subject to an incident plane wave, using an array of secondary sources in the aperture. In this case the diffraction through the aperture becomes important when its size is compatible with the acoustic wavelength, in which case only a few sources are necessary for good control. When the size of the aperture is large compared to the wavelength, and diffraction is less important but more secondary sources need to be used for good control, the results then become similar to those for the free field problem with an infinite source array.

Text Wavenumber_Approach - Accepted Manuscript
Restricted to Repository staff only until 10 April 2019.
Request a copy

More information

Accepted/In Press date: 10 January 2018
e-pub ahead of print date: 12 February 2018
Published date: 14 April 2018

Identifiers

Local EPrints ID: 416922
URI: https://eprints.soton.ac.uk/id/eprint/416922
ISSN: 0022-460X
PURE UUID: 7bfdee2d-6367-44aa-895b-5a5cd70fcc3c
ORCID for Jordan Cheer: ORCID iD orcid.org/0000-0002-0552-5506

Catalogue record

Date deposited: 15 Jan 2018 17:30
Last modified: 06 Jun 2018 12:32

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×