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The branch structure of embedded trapped modes in two-dimensional waveguides

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posted on 2006-02-06, 17:18 authored by Maureen McIver, Christopher LintonChristopher Linton, J. Zhang
In this paper we investigate the existence of branches of embedded trapped modes in the vicinity of symmetric obstacles which are placed on the centreline of a twodimensional acoustic waveguide. Modes are sought which are antisymmetric about the centreline of the channel and which have frequencies that are above the first cut-off for antisymmetric wave propagation down the guide. In previous work [1], a procedure for finding such modes was developed and it was shown numerically that a branch of trapped modes exists for an ellipse which starts from a flat plate on the centreline of the guide and terminates with a flat plate perpendicular to the guide walls. In this work we show that further branches of such modes exist for both ellipses and rectangular blocks, each of which starts with a plate of different length on the centreline of the guide. Approximations to the trapped mode wave numbers for rectangular blocks are derived from a two-term matched eigenfunction expansion and these are compared to the results from the numerical scheme described in [1]. The transition from trapped mode to standing wave which occurs at one end of each of the branches is investigated in detail.

History

School

  • Science

Department

  • Mathematical Sciences

Pages

154832 bytes

Publication date

2000

Notes

This is a pre-print. The definitive version: McIVER, M., LINTON, C.M. and ZHANG, J., 2002. The branch structure of embedded trapped modes in two-dimensional waveguides. Quarterly Journal of Mechanics and Applied Mathematics, 55, Part 2, pp. 313-326

Language

  • en