Analytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls: Application to a triangular duct

作者：Lawrie Jane B^*

来源：Wave Motion, 2013, 50(3): 542-557.

DOI：10.1016/j.wavemoti.2012.12.002

• Three dimensional duct
• Flexible walls
• Elastic plate
• Triangular cross-section
• Mode-matching
• Acoustic propagation

An 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 %26quot;junction%26quot; conditions.

• 出版日期2013-4