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Fast Computation of the Scattering Matrix of Lined Ducts Containing Passive Components

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This paper deals with strategies for computing efficiently the propagation of sound waves in lined ducts containing passive components. In most cases of practical interest, these added acoustics components can be modelled as acoustic cavities which are connected to the duct and can be either purely reactive or dissipative. The assessment of the efficiency of such a system requires a precise knowledge of the acoustic field in the duct. In the present work a new numerical procedure that judiciously exploit the benefit of the FEM and the mode matching approach is presented. First, a set of FE eigenmode are computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. The presence of acoustic liners on the walls of the duct is taken into account via an appropriate modal decomposition of the Green's function. Typical applications involving Helmholtz resonators and side branch ducts (Herschel-Quincke tubes) are presented. We show that our algorithm allows a very fast and accurate computation of the scattering matrix of such a system with a numerical complexity that grows very mildly with the frequency.
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Document Type: Research Article

Publication date: 2011-11-01

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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