Comptes Rendus
Oscillations of two superposed fluids in an open and flexible container
Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 329-335.

The interaction of two superposed inviscid liquids with a flexible side wall of a rectangular container is considered. The governing equations describing the behaviour of the system are analyzed using the concept of normal modes, and their solutions presented in the form of infinite series. The expansion coefficients for the velocity potentials are calculated by employing a new inner product which allows orthogonalizing the fluid shape modes. An eigenfrequency equation is then derived from the requirement for a nontrivial solution exists. The influence of the governing parameters on the coupled frequencies is illustrated in the case of water–mercury system.

On établit une équation permettant de calculer les fréquences de couplage d'une paroi flexible d'un réservoir rectangulaire contenant deux fluides parfaits, non miscibles, avec surface libre. La procédure utilisée est basée sur une décomposition en modes normaux et l'établissement d'un produit scalaire approprié orthogonalisant la suite des modes normaux pour les potentiels des vitesses. Une application numérique est donnée dans le cas du système mercure–eau.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2007.10.020
Keywords: Fluid mechanics, Flexible wall, Coupled frequencies
Mot clés : Mécanique des fluides, Paroi flexible, Fréquences de couplage

Mustapha Amaouche 1; Bachir Meziani 1

1 Laboratoire de physique théorique, Université A. Mira de Béjaia, route de Targua Ouzemmour, 06000 Béjaia, Algeria
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Mustapha Amaouche; Bachir Meziani. Oscillations of two superposed fluids in an open and flexible container. Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 329-335. doi : 10.1016/j.crme.2007.10.020. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.020/

[1] J.W. Miles On the sloshing of liquid in a flexible tank, J. Appl. Mech., Volume 25 (1958), pp. 277-283

[2] H.F. Bauer Hydroelastic vibrations in a rectangular container, Int. J. Solids and Structure, Volume 17 (1981), pp. 639-707

[3] X.J. Chai; J.M. Geneveaux; J.P. Brancher Fluid–solid interaction in a rectangular container, Eur. J. Mech. B/Fluids, Volume 15 (1996), pp. 863-883

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