Spectral asymptotics of the Helmholtz model in fluid-solid structures

Allaire, G. ; Conca, C. ; Vanninathan, M. (1999) Spectral asymptotics of the Helmholtz model in fluid-solid structures International Journal for Numerical Methods in Engineering, 46 (9). pp. 1463-1504. ISSN 0029-5981

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1...

Related URL: http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1463::AID-NME708>3.0.CO;2-9


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.

Item Type:Article
Source:Copyright of this article belongs to John Wiley and Sons.
Keywords:Homogenization; Bloch Waves; Spectral Analysis; Fluid-solid Structures
ID Code:55389
Deposited On:18 Aug 2011 07:05
Last Modified:18 Aug 2011 07:05

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