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Title: Mode-matching without root-finding: Application to a dissipative silencer
Authors: Lawrie, JB
Kirby, R
Keywords: Mode matching;Dissipative silencer;Root finding;HVAC silencer
Issue Date: 2006
Publisher: American Institute of Physics
Citation: Journal of the Acoustical Society of America, 119(4): 2050-2061, Apr 2006
Abstract: This article presents an analytic mode-matching approach suitable for modelling the propagation of sound in a two-dimensional, three-part, ducting system. The approach avoids the need to the find roots of the characteristic equation for the middle section of the duct (the component) and is readily applicable to a broad class of problems. It is demonstrated that the system of equations, derived via analytic mode-matching, exhibits certain features which ensure that they can be re-cast into a form that is independent of the roots of the characteristic equation for the component. The precise details of the component are irrelevant to the procedure; it is required only that there exists an orthogonality relation, or similar, for the eigenmodes corresponding to the propagating wave-forms in this region. The method is applied here to a simple problem involving acoustic transmission through a dissipative silencer of the type commonly found in heating ventilation and air-conditioning (HVAC) ducts. With reference to this example, the silencer transmission loss is computed, and the power balance for the silencer is investigated and is shown to be an identity that is necessarily satisfied by the system of equations, regardless of the level of truncation.
ISSN: 0001-4996
Appears in Collections:Mechanical and Aerospace Engineering
Dept of Mechanical Aerospace and Civil Engineering Research Papers
Dept of Mathematics Research Papers
Mathematical Sciences

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