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Trapped modes and Fano resonances in two-dimensional acoustical duct–cavity systems

Published online by Cambridge University Press:  05 January 2012

Stefan Hein ,
Werner Koch  and
Lothar Nannen
Stefan Hein
Affiliation:
Institut für Aerodynamik und Strömungstechnik, DLR Göttingen, 37073 Göttingen, Germany
Werner Koch*
Affiliation:
Institut für Aerodynamik und Strömungstechnik, DLR Göttingen, 37073 Göttingen, Germany
Lothar Nannen
Affiliation:
Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083 Göttingen, Germany
*
†Email address for correspondence: werner.koch@dlr.de
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Abstract

Revisiting the classical acoustics problem of rectangular side-branch cavities in a two-dimensional duct of infinite length, we use the finite-element method to numerically compute the acoustic resonances as well as the sound transmission and reflection for an incoming fundamental duct mode. To satisfy the requirement of outgoing waves in the far field, we use two different forms of absorbing boundary conditions, namely the complex scaling method and the Hardy space method. In general, the resonances are damped due to radiation losses, but there also exist various types of localized trapped modes with nominally zero radiation loss. The most common type of trapped mode is antisymmetric about the duct axis and becomes quasi-trapped with very low damping if the symmetry about the duct axis is broken. In this case a Fano resonance results, with resonance and antiresonance features and drastic changes in the sound transmission and reflection coefficients. Two other types of trapped modes, termed embedded trapped modes, result from the interaction of neighbouring modes or Fabry–Pérot interference in multi-cavity systems. These embedded trapped modes occur only for very particular geometry parameters and frequencies and become highly localized quasi-trapped modes as soon as the geometry is perturbed. We show that all three types of trapped modes are possible in duct–cavity systems and that embedded trapped modes continue to exist when a cavity is moved off centre. If several cavities interact, the single-cavity trapped mode splits into several trapped supermodes, which might be useful for the design of low-frequency acoustic filters.

JFM classification

Acoustics: Acoustics Acoustics: Noise control Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 692 , 10 February 2012 , pp. 257 - 287
Copyright
Copyright © Cambridge University Press 2012

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