Spectral asymptotics of the Helmholtz model in fluid-solid structures

被引:0
|
作者
Allaire, G
Conca, C
Vanninathan, M
机构
[1] Univ Chile, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, Santiago, Chile
[2] Univ Paris 06, Anal Numer Lab, F-75252 Paris, France
[3] Indian Inst Sci, TIFR Math Programme, TIFR Ctr, Bangalore 560012, Karnataka, India
关键词
homogenization; Bloch waves; spectral analysis; fluid-solid structures;
D O I
10.1002/(SICI)1097-0207(19991130)46:9<1463::AID-NME708>3.0.CO;2-9
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A model representing the vibrations of a coupled fluid-solid structure is considered. This structure consists of a tube bundle immersed in a slightly compressible fluid. Assuming periodic distribution of tubes, this article describes the asymptotic nature of the vibration frequencies when the number of tubes is large. Our investigation shows that classical homogenization of the problem is not sufficient for this purpose. Indeed, our end result proves that the limit spectrum consists of three parts: the macro-part which comes from homogenization, the micro-part and the boundary layer part. The last two components are new. We describe in detail both macro- and micro-parts using the so-called Bloch wave homogenization method. Copyright (C) 1999 John Wiley & Sons, Ltd.
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页码:1463 / 1504
页数:42
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