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Journal Articles SIAM Journal on Applied Mathematics Year : 2013

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

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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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Dates and versions

hal-00860712 , version 1 (10-09-2013)

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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, 2013, 73 (1), pp.438-459. ⟨10.1137/120867123⟩. ⟨hal-00860712⟩
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