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.
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Mots-clés : Milieux continus, Couplages fluide–structure, Semi-groupes non-linéaires
Christian Licht 1; Tran Thu Ha 2
@article{CRMECA_2005__333_2_117_0, author = {Christian Licht and Tran Thu Ha}, title = {Small vibrations of a linearly elastic body surrounded by heavy, incompressible, {non-Newtonian} fluids with free surfaces}, journal = {Comptes Rendus. M\'ecanique}, pages = {117--122}, publisher = {Elsevier}, volume = {333}, number = {2}, year = {2005}, doi = {10.1016/j.crme.2004.09.011}, language = {en}, }
TY - JOUR AU - Christian Licht AU - Tran Thu Ha TI - Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces JO - Comptes Rendus. Mécanique PY - 2005 SP - 117 EP - 122 VL - 333 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2004.09.011 LA - en ID - CRMECA_2005__333_2_117_0 ER -
%0 Journal Article %A Christian Licht %A Tran Thu Ha %T Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces %J Comptes Rendus. Mécanique %D 2005 %P 117-122 %V 333 %N 2 %I Elsevier %R 10.1016/j.crme.2004.09.011 %G en %F CRMECA_2005__333_2_117_0
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] 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] Added mass and damping in fluid–structure interaction, Comput. Methods Appl. Mech. Engrg., Volume 146 (1997), pp. 387-405
[3] Opérateurs maximaux-monotones et semi-groupes non-linéaires de contraction, North–Holland, 1973
[4] Problèmes mathématiques en plasticité, Gauthier-Villars, 1983
[5] Approximation of semi-groups of operators, Pacific J. Math., Volume 28 (1958), pp. 887-919
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