%0 Journal Article
%T Resonances of an elastic plate coupled with a compressible confined flow
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%A Bonnet-Ben Dhia, Anne-Sophie
%A Mercier, Jean-François
%< avec comité de lecture
%@ 0033-5614
%J Quarterly Journal of Mechanics and Applied Mathematics
%I Oxford University Press (OUP)
%V 62
%N 2
%P 105-129
%8 2009
%D 2009
%R 10.1093/qjmam/hbp004
%K Borne inférieure
%K Opérateur autoadjoint
%K Problème valeur propre
%K Modélisation
%K Plaque
%K Fluide compressible
%K Fréquence résonance
%K Interaction fluide structure
%K Écoulement conduite
%K Écoulement compressible
%K Résonance
%Z Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]Journal articles
%X A theoretical study of the resonances of an elastic plate in a compressible flow in a two-dimensional duct is presented. Due to the fluid-structure coupling, a quadratic eigenvalue problem is involved, in which the resonance frequencies k solve the equations λ(k) = k2, where λ is the eigenvalue of a self-adjoint operator of the form A + kB. In a previous paper, we have proved that a linear eigenvalue problem is recovered if the plate is rigid or the fluid at rest. We focus here on the general problem for which elasticity and flow are jointly present and derive a lower bound for the number of resonances. The expression of this bound, based on the solution of two linear eigenvalue problems, points out that the coupling between elasticity and flow generally reduces the number of resonances. This estimate is validated numerically. © The author 2009. Published by Oxford University Press; all rights reserved.
%G English
%L hal-00873072
%U https://ensta-paris.hal.science/hal-00873072
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