Trapped modes in acoustic waveguides

1 August 1998

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 51 (3) , 477-492
https://doi.org/10.1093/qjmam/51.3.477

Abstract

We consider the eigenvalue problem for the Laplacian on a cylinder perturbed by a compact obstacle (with Neumann boundary conditions) and look for eigenvalues of such a problem. In the case of a two-dimensional cylinder with symmetric obstacle we give sufficient conditions for both existence and non-existence of an eigenvalue. We also prove that in the case of a thin obstacle, parallel to the axis of the cylinder, there always exists an eigenvalue.

Keywords

EIGENVALUE
SUFFICIENT CONDITIONS
ACOUSTIC WAVEGUIDES
TRAPPED MODES
GIVE SUFFICIENT
COMPACT OBSTACLE
CYLINDER PERTURBED
DIMENSIONAL CYLINDER
SYMMETRIC OBSTACLE

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