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Title: | Orthogonality relations for fluid-structural waves in a 3-D rectangular duct with flexible walls |
Authors: | Lawrie, JB |
Keywords: | Three-dimensional waveguide;Flexible wall;Elastic plate;Orthogonality relation;Acoustic scattering;Mode-matching |
Issue Date: | 27-May-2009 |
Publisher: | The Royal Society |
Citation: | Lawrie, J.B. (2009) 'Orthogonality relations for fluid-structural waves in a 3-D rectangular duct with flexible walls', Proceedings of the Royal Society A. 365 (2108), pp. 2347-2367. doi: 10.1098/rspa.2009.0066. |
Abstract: | An exact expression for the fluid-coupled structural waves that propagate in a three-dimensional, rectangular waveguide with elastic walls is presented in terms of the non-separable eigenfunctions ψn(y,z). It is proved that these eigenfunctions are linearly dependent and that an eigenfunction expansion representation of a suitably smooth function f(y,z) converges point-wise to that function. Orthogonality results for the derivatives ψny(a,z) are derived which, together with a partial orthogonality relation for ψn(y,z), enable the solution of a wide range of acoustic scattering problems. Two prototype problems, of the type typically encountered in two-part scattering problems, are solved, and numerical results showing the displacement of the elastic walls are presented. |
URI: | https://bura.brunel.ac.uk/handle/2438/3464 |
DOI: | https://doi.org/10.1098/rspa.2009.0066 |
ISSN: | 1364-5021 |
Appears in Collections: | Brunel OA Publishing Fund Dept of Mathematics Research Papers Mathematical Sciences |
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Orthogonality relations for fluid-structural waves in a 3-D rectangular duct with flexible walls.pdf | Copyright © 2009 The Royal Society. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | 311.58 kB | Adobe PDF | View/Open |
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