Resonances of an elastic plate in a compressible confined fluid

Anne-Sophie Bonnet-Ben Dhia 1 Jean-François Mercier 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We present a theoretical study of the resonances of a fluid-structure problem, an elastic plate placed in a duct in the presence of a compressible fluid. The case of a rigid plate has been largely studied. Acoustic resonances are then associated to resonant modes trapped by the plate. Due to the elasticity of the plate, we need to solve a quadratic eigenvalue problem in which the resonance frequencies k solve the equations γ(k) = k2, where γ are the eigenvalues of a self-adjoint operator of the form A + kB. First, we show how to study the eigenvalues located below the essential spectrum by using the min-max principle. Then, we study the fixed-point equations. We establish sufficient conditions on the characteristics of the plate and of the fluid to ensure the existence of resonances. Such conditions are validated numerically. © The author 2007. Published by Oxford University Press; all rights reserved.
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Submitted on : Thursday, October 24, 2013 - 11:15:14 AM
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Anne-Sophie Bonnet-Ben Dhia, Jean-François Mercier. Resonances of an elastic plate in a compressible confined fluid. Quarterly Journal of Mechanics and Applied Mathematics, Oxford University Press (OUP), 2007, 60 (4), pp.397-421. ⟨10.1093/qjmam/hbm015⟩. ⟨hal-00876224⟩

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