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

Hein, Stefan and Koch, Werner and Nannen, Lothar (2012) Trapped modes and Fano resonances in two-dimensional acoustical duct-cavity systems. Journal of Fluid Mechanics, Vol. 692, pp. 257-287. Cambidge University Press. doi: 10.1017/jfm.2011.509. ISSN 0022-1120.

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Official URL: http://journals.cambridge.org/action//displayAbstract?fromPage=online&aid=8478295&fulltextType=RA&fileId=S002211201100509X


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 coefficient. Two other types of trapped modes, termed embedded trapped modes, result from the interaction of neighbouring modes or Fabry–P´erot 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.

Item URL in elib:https://elib.dlr.de/70256/
Document Type:Article
Title:Trapped modes and Fano resonances in two-dimensional acoustical duct-cavity systems
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Nannen, LotharGeorg-August-Universität GöttingenUNSPECIFIED
Date:January 2012
Journal or Publication Title:Journal of Fluid Mechanics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Volume:Vol. 692
DOI :10.1017/jfm.2011.509
Page Range:pp. 257-287
Publisher:Cambidge University Press
Keywords:acoustics, duct, cavity, trapped mode, Fano resonance, scattering, perfectly matched layer (PML), Hardy space method
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Flight Physics (old)
Location: Göttingen
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > High Speed Configurations
Deposited By: Hein, Dr.-Ing. Stefan
Deposited On:07 Feb 2012 08:02
Last Modified:08 Mar 2018 18:43

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