MATHEMATICAL JUSTIFICATION OF THE RAYLEIGH CONDUCTIVITY MODEL FOR PERFORATED PLATES IN ACOUSTICS

被引：8

作者：

Bendali, Abderrahmane ^{[1
,2
]}

Fares, M'Barek ^{[2
]}

Piot, Estelle ^{[3
]}

Tordeux, Sebastien ^{[2
,4
]}

机构：

[1] Univ Toulouse, Inst Math Toulouse, Dept Genie Math, INSA Toulouse, F-31077 Toulouse 4, France

[2] CERFACS, F-31057 Toulouse 1, France

[3] Off Natl Etud & Rech Aerosp, Toulouse, France

[4] Univ Pau & Pays Adour, CNRS UMR 5142, Project Team Magique 3D, INRIA Bordeaux Sud Ouest,LMA Pau,IPRA, F-64013 Pau, France

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2013年 / 73卷 / 01期

关键词：

multiperforated plates; acoustics; effective transmission conditions; Helmholtz equation; Rayleigh conductivity; matched asymptotic expansions; quasi-periodic waves; lattice sums; BIAS-FLOW; ABSORPTION; IMPEDANCE; WAVES; MEDIA; SOUND;

D O I：

10.1137/120867123

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：438 / 459

页数：22

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