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Title: On acoustic propagation in three-dimensional rectangular ducts with flexible walls and porous linings
Authors: Lawrie, JB
Keywords: Acoustic wave propagation;Ducts;Eigenvalues and eigenfunctions;Fourier series;Porous materials;Structural acoustics
Issue Date: 2012
Publisher: Acoustical Society of America
Citation: Journal of the Acoustical Society of America, 131(3): 1890 - 1901, Mar 2012
Abstract: The focus of this article is toward the development of hybrid analytic-numerical mode-matching methods for model problems involving three-dimensional ducts of rectangular cross-section and with flexible walls. Such methods require first closed form analytic expressions for the natural fluid-structure coupled waveforms that propagate in each duct section and second the corresponding orthogonality relations. It is demonstrated how recent theory [Lawrie, Proc. R. Soc. London, Ser. A 465, 2347–2367 (2009)] may be extended to a wide class of three-dimensional ducts, for example, those with a flexible wall and a porous lining (modeled as an equivalent fluid) or those with a flexible internal structure, such as a membrane (the “drum-like” silencer). Two equivalent expressions for the eigenmodes of a given duct can be formulated. For the ducts considered herein, the first ansatz is dependent on the eigenvalues/eigenfunctions appropriate for wave propagation in the corresponding two-dimensional flexible-walled duct, whereas the second takes the form of a Fourier series. The latter offers two advantages: no “root-finding” is involved and the method is appropriate for ducts in which the flexible wall is orthotropic. The first ansatz, however, provides important information about the orthogonality properties of the three-dimensional eigenmodes.
Description: This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 Acoustical Society of America
ISSN: 0001-4966
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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