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Modal Solutions in Circular and Annular Ducts with Locally or Bulk Reacting Lining

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In circular and annular lined ducts there exist modes of the sound field in both azimutal and radial directions. There are two distinct tasks to be solved for technical applications. In the first task, one is interested in the attenuation of the least attenuated mode because this mode determines the sound reduction under general conditions of excitation. The second task aims at the computation of a set of modes. The solutions of this task are needed in a modal analysis of sound fields in structured round silencers, the modes being orthogonal to each other. It is sufficient in the first task to look for the least attenuated mode among the two first radial modes. A set of modes for a modal analysis must be unique in the sense that no mode solution appears twice in the set of solutions and that no mode is missing in a set extending up to a given order. Otherwise the systems of equations for the amplitudes of the modes in the further analysis would become singular. Therefore, the problem of the limits between the modes must be solved and/or safe algorithms for modal solutions should be available. Both problems will be tackled in the present paper. The numerical difficulties increase at the transitions from locally reacting linings to bulk reacting linings and from circular to annular ducts. The present analysis assumes no mean flow in the duct. The solutions under this condition serve as start solutions in numerical algorithms for the modal solutions with flow.
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Document Type: Research Article

Publication date: 01 March 1998

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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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