Spectral asymptotics of the Helmholtz model in fluid–solid structures
Article first published online: 19 OCT 1999
Copyright © 1999 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Special Issue: Papers presented at the Fourth World Congress on Computational Mechanics (IV WCCM), Buenos Aires, Argentina, 29 June–2 July 1998. Solid and Fluid Numerical Models for Advanced Engineering Problems
Volume 46, Issue 9, pages 1463–1504, 30 November 1999
How to Cite
Allaire, G., Conca, C. and Vanninathan, M. (1999), Spectral asymptotics of the Helmholtz model in fluid–solid structures. Int. J. Numer. Meth. Engng., 46: 1463–1504. doi: 10.1002/(SICI)1097-0207(19991130)46:9<1463::AID-NME708>3.0.CO;2-9
- Issue published online: 19 OCT 1999
- Article first published online: 19 OCT 1999
- Manuscript Revised: 1 FEB 1999
- Manuscript Received: 1 SEP 1998
- bloch waves;
- spectral analysis;
- fluid–solid structures
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 © 1999 John Wiley & Sons, Ltd.