Analytical model of a finite length rectangular duct with bulk-reacting lining
Analytical model of a finite length rectangular duct with bulk-reacting lining
The focus of this work is on analytical modelling of sound transmission along a lined duct. The duct of interest has a rectangular cross-section as normally used for ventilation purposes. The mean flow in a ventilation duct is very low and can be neglected. In this paper, a two-dimensional analytical model is developed for sound transmission through a finite length of duct lined with bulk-reacting material. The analytical model is developed using the mode-matching technique and the required finite number of wavenumbers are tracked using Müller’s method. The wavenumbers are tracked from a very low frequency to high frequency using small frequency steps. It is found that, for a duct with a bulk-reacting lining, the number of modes with a transverse wavenumber below a particular value may exceed the corresponding number of modes in a duct with a locally-reacting lining. These additional modes are termed lining modes and these modes depend on the lining thickness. Dispersion curves are presented for both types of mode, the airway modes and the lining modes. The mode-matching technique allows analysis of multi-modal wave propagation in the duct. The model is developed for an infinitely long rigid duct with a finite length of lined insert. The estimation of transmission loss from the locally reacting model, that is widely available in the literature, is compared with the transmission loss estimated from the newly developed bulk reacting model. Although the locally reacting model often overestimates the performance of a bulk-reacting lining it is found that this is not always the case, especially at low and high frequencies
ramli, Nabilah
502dea91-b49c-4a1b-a71c-6bf2ed6d0bcc
Thompson, D.J.
bca37fd3-d692-4779-b663-5916b01edae5
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
2013
ramli, Nabilah
502dea91-b49c-4a1b-a71c-6bf2ed6d0bcc
Thompson, D.J.
bca37fd3-d692-4779-b663-5916b01edae5
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
ramli, Nabilah, Thompson, D.J. and Waters, T.P.
(2013)
Analytical model of a finite length rectangular duct with bulk-reacting lining.
20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand.
06 - 10 Jul 2013.
Record type:
Conference or Workshop Item
(Paper)
Abstract
The focus of this work is on analytical modelling of sound transmission along a lined duct. The duct of interest has a rectangular cross-section as normally used for ventilation purposes. The mean flow in a ventilation duct is very low and can be neglected. In this paper, a two-dimensional analytical model is developed for sound transmission through a finite length of duct lined with bulk-reacting material. The analytical model is developed using the mode-matching technique and the required finite number of wavenumbers are tracked using Müller’s method. The wavenumbers are tracked from a very low frequency to high frequency using small frequency steps. It is found that, for a duct with a bulk-reacting lining, the number of modes with a transverse wavenumber below a particular value may exceed the corresponding number of modes in a duct with a locally-reacting lining. These additional modes are termed lining modes and these modes depend on the lining thickness. Dispersion curves are presented for both types of mode, the airway modes and the lining modes. The mode-matching technique allows analysis of multi-modal wave propagation in the duct. The model is developed for an infinitely long rigid duct with a finite length of lined insert. The estimation of transmission loss from the locally reacting model, that is widely available in the literature, is compared with the transmission loss estimated from the newly developed bulk reacting model. Although the locally reacting model often overestimates the performance of a bulk-reacting lining it is found that this is not always the case, especially at low and high frequencies
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Published date: 2013
Venue - Dates:
20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 2013-07-06 - 2013-07-10
Organisations:
Mathematical Sciences, Dynamics Group
Identifiers
Local EPrints ID: 356784
URI: http://eprints.soton.ac.uk/id/eprint/356784
PURE UUID: 7b1d83c7-f794-4c2f-890a-6502ca70ad66
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Date deposited: 16 Sep 2013 10:31
Last modified: 09 Jan 2022 02:51
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Contributors
Author:
Nabilah ramli
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