Spectral asymptotics of the Helmholtz model in fluid-solid structures

Allaire, G and Conca, Carlos and Vanninathan, M (1999) Spectral asymptotics of the Helmholtz model in fluid-solid structures. In: International Journal for Numerical Methods in Engineering, 46 (9). pp. 1463-1504.

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Abstract

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.

Item Type:	Journal Article
Publication:	International Journal for Numerical Methods in Engineering
Publisher:	John Wiley and Sons
Additional Information:	Copyright of this article belongs to John Wiley and Sons.
Keywords:	homogenization;bloch waves;spectral analysis;uid{solid structures
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 Jun 2011 13:54
Last Modified:	01 Mar 2019 09:53
URI:	http://eprints.iisc.ac.in/id/eprint/38776

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