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Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition
Jönköping University, School of Engineering, JTH, Mathematics.
International Centre for Mathematical modelling, Växjö University.
2008 (English)In: International Conference on Numerical Analysis and Applied Mathematics 2008, Melville: American Institute of Physics , 2008, 33-36 p.Conference paper, Published paper (Refereed)
Abstract [en]

Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.

Place, publisher, year, edition, pages
Melville: American Institute of Physics , 2008. 33-36 p.
Series
AIP Conference Proceedings, ISSN 0094-243X ; 1048
Keyword
acoustic scattering, waveguide scattering, impedance, Building Block Method, numerical conformal mapping, Outer Polygon Method, invariant embedding
National Category
Fluid Mechanics and Acoustics Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-6650DOI: 10.1063/1.2990928 ISBN: 978-0-7354-0576-9 (print)OAI: oai:DiVA.org:hj-6650DiVA: diva2:113812
Available from: 2008-10-28 Created: 2008-10-28 Last updated: 2009-01-28Bibliographically approved

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Publisher's full texthttp://link.aip.org/link/?APCPCS/1048/33/1

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CiteExportLink to record
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Citation style
  • apa
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  • modern-language-association-8th-edition
  • vancouver
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More styles
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  • de-DE
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Output format
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