%0 Journal Article
%T Resonances of an elastic plate in a compressible confined fluid
%+ 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 60
%N 4
%P 397-421
%8 2007
%D 2007
%R 10.1093/qjmam/hbm015
%Z Mathematics [math]/Numerical Analysis [math.NA]
%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 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.
%G English
%L hal-00876224
%U https://hal-ensta-paris.archives-ouvertes.fr//hal-00876224
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