Comptes Rendus
no. 8
Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow
Grigory P. Panasenko1  ; Ruxandra Stavre2
1 Institute Camille-Jordan, UMR CNRS 5208, PRES University of Lyon, University of Saint-Etienne, 23, rue Dr Paul-Michelon, 42023 Saint-Etienne, France
2 Institute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 590-595.

The interaction “viscous fluid–thin plate” is considered when the thickness of the plate, ε, tends to zero, while the density and the Youngʼs modulus of the plate are of order ε−1 and ε−3, respectively. The thickness of the fluid layer is of the order of one. An asymptotic expansion is constructed and the error estimates are proved. The leading term of the asymptotic expansion is the solution of the interaction problem “fluid-Kirchoff plate”. The method of asymptotic partial domain decomposition is discussed: the main part of the plate is described by a 1D model while a small part is simulated by the 2D elasticity equations, with appropriate junction conditions.

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DOI : 10.1016/j.crme.2012.06.001
Mots clés : Fluid mechanics, Dynamical systems, Fluid structure interaction, Asymptotic analysis
Grigory P. Panasenko 1 ; Ruxandra Stavre 2

1 Institute Camille-Jordan, UMR CNRS 5208, PRES University of Lyon, University of Saint-Etienne, 23, rue Dr Paul-Michelon, 42023 Saint-Etienne, France
2 Institute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania 
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Grigory P. Panasenko; Ruxandra Stavre. Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow. Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 590-595. doi : 10.1016/j.crme.2012.06.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.06.001/

[1] G.P. Panasenko; R. Stavre Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl., Volume 85 (2006), pp. 558-579

[2] G. Panasenko Multi-Scale Modelling for Structures and Composites, Springer, 2005

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