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dc.contributor.authorLawrie, JB-
dc.identifier.citationWave Motion, 50(3): 542–557, Apr 2013en_US
dc.descriptionThis is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 Elsevieren_US
dc.description.abstractAn analytic mode-matching method suitable for the solution of problems involving scattering in three-dimensional waveguides with flexible walls is presented. Prerequisite to the development of such methods is knowledge of closed form analytic expressions for the natural fluid–structure coupled waveforms that propagate in each duct section and the corresponding orthogonality relations. In this article recent theory [J.B. Lawrie, Orthogonality relations for fluid–structural waves in a 3-D rectangular duct with flexible walls, Proc. R. Soc. A. 465 (2009) 2347–2367] is extended to construct the non-separable eigenfunctions for acoustic propagation in a three-dimensional rectangular duct with four flexible walls. For the special case in which the duct cross-section is square, the symmetrical nature of the eigenfunctions enables the eigenmodes for a right-angled, isosceles triangular duct with flexible hypotenuse to be deduced. The partial orthogonality relation together with other important properties of the triangular modes are discussed. A mode-matching solution to the scattering of a fluid–structure coupled wave at the junction of two identical semi-infinite ducts of triangular cross-section is demonstrated for two different sets of “junction” conditions.en_US
dc.subjectThree dimensional ducten_US
dc.subjectFlexible wallsen_US
dc.subjectElastic plateen_US
dc.subjectTriangular cross-sectionen_US
dc.subjectAcoustic propagationen_US
dc.titleAnalytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls: Application to a triangular ducten_US
pubs.organisational-data/Brunel/Brunel Active Staff-
pubs.organisational-data/Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths-
pubs.organisational-data/Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths/Maths-
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Dept of Mathematics Research Papers
Mathematical Sciences

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