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 solut...
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| Published in | Journal of sound and vibration Vol. 419; pp. 405 - 419 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Ltd
14.04.2018
Elsevier Science Ltd |
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| Online Access | Get full text |
| ISSN | 0022-460X 1095-8568 1095-8568 |
| DOI | 10.1016/j.jsv.2018.01.028 |
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| 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. |
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| AbstractList | 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. |
| Author | Gan, Woon-Seng Cheer, Jordan Bhan, Lam Elliott, Stephen J. Shi, Chuang |
| Author_xml | – sequence: 1 givenname: Stephen J. surname: Elliott fullname: Elliott, Stephen J. email: s.j.elliott@soton.ac.uk organization: Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton, SO17 1BJ, UK – sequence: 2 givenname: Jordan surname: Cheer fullname: Cheer, Jordan email: j.cheer@soton.ac.uk organization: Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton, SO17 1BJ, UK – sequence: 3 givenname: Lam surname: Bhan fullname: Bhan, Lam organization: Digital Signal Processing Lab, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore – sequence: 4 givenname: Chuang surname: Shi fullname: Shi, Chuang organization: School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China – sequence: 5 givenname: Woon-Seng surname: Gan fullname: Gan, Woon-Seng organization: Digital Signal Processing Lab, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore |
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| Keywords | Feedforward control Wavenumber domain Active noise control |
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| SubjectTerms | Acoustic emission testing Acoustics Active control Active noise control Arrays Braided composites Computer simulation Diffraction Feedforward control Incident waves Materials science Microphones Plane waves Sound waves Wave division multiplexing Wavelengths Wavenumber domain |
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| Title | A wavenumber approach to analysing the active control of plane waves with arrays of secondary sources |
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