Comptes Rendus
Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces
Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 117-122.

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity.

On considère les petits mouvements instationnaires d'un système couplé constitué d'un solide linéairement élastique et de deux fluides non-Newtoniens, incompressibles, pesants à surfaces libres. Une formulation en termes d'équations d'évolution non-linéaires dans des espaces de Hilbert d'états possibles d'énergie mécanique finie permet d'obtenir des résultats d'existence et d'unicité et d'étudier l'influence de la gravité.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.09.011
Keywords: Continuum Mechanics, Fluid–structure interactions, Non-linear semi-groups
Mot clés : Milieux continus, Couplages fluide–structure, Semi-groupes non-linéaires

Christian Licht 1; Tran Thu Ha 2

1 Laboratoire de mécanique et génie civil, UMR 5508 CNRS, université Montpellier 2, case courrier 048, place Eugène Bataillon, 34095 Montpellier cedex 05, France
2 Institute of Mechanics of Hanoi, 264 Doi Can St., Hanoi, Viet Nam
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Christian Licht; Tran Thu Ha. Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces. Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 117-122. doi : 10.1016/j.crme.2004.09.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.09.011/

[1] M.B. Orazov Localization of the spectrum in the problem of normal oscillations of an elastic shell filled with a viscous incompressible fluid, Comput. Math. Math. Phys. (USSR), Volume 25 (1985), pp. 52-58

[2] C. Conca; A. Osses; J. Planchard Added mass and damping in fluid–structure interaction, Comput. Methods Appl. Mech. Engrg., Volume 146 (1997), pp. 387-405

[3] H. Brezis Opérateurs maximaux-monotones et semi-groupes non-linéaires de contraction, North–Holland, 1973

[4] R. Temam Problèmes mathématiques en plasticité, Gauthier-Villars, 1983

[5] H.F. Trotter Approximation of semi-groups of operators, Pacific J. Math., Volume 28 (1958), pp. 887-919

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