Mathematical justification of the Rayleigh conductivity model for perforated plates in acoustics

Abstract : This paper is devoted to the mathematical justification of the usual models predicting the effective reflection and transmission of an acoustic wave by a low porosity multiperforated plate. Some previous intuitive approximations require that the wavelength be large compared with the spacing separating two neighboring apertures. In particular, we show that this basic assumption is not mandatory. Actually, it is enough to assume that this distance is less than a half-wavelength. The main tools used are the method of matched asymptotic expansions and lattice sums for the Helmholtz equations. Some numerical experiments illustrate the theoretical derivations.
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Journal articles
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https://hal.inria.fr/hal-00860712
Contributor : Sébastien Tordeux <>
Submitted on : Tuesday, September 10, 2013 - 9:56:57 PM
Last modification on : Thursday, October 17, 2019 - 8:57:40 AM

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Abderrahmane Bendali, M'Barek Fares, Estelle Piot, Sébastien Tordeux. Mathematical justification of the Rayleigh conductivity model for perforated plates in acoustics. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2013, 73 (1), pp.438-459. ⟨10.1137/120867123⟩. ⟨hal-00860712⟩

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