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A Sufficient Condition for the Absence of Two-Dimensional Instabilities of an Elastic Plate in a Duct with Compressible Flow

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 study the time-harmonic resonance of a finite-length elastic plate in a fluid in 5 uniform flow confined in a duct. Although the resonance frequencies are usually real, the combined 6 effects of plate elasticity and of a flow can create complex frequencies, different from the usual so-7 called scattering frequencies, corresponding to instabilities. We study theoretically the existence of 8 instabilities versus several problem parameters, notably the flow velocity and the ratio of densities 9 and of sound speeds between the plate and the fluid. A 3D-volume in the parameters space is defined, 10 in which no instability can develop. In particular it corresponds to a low enough velocity or a light 11 enough plate. The theoretical estimates are validated numerically. 12
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Jean-François Mercier. A Sufficient Condition for the Absence of Two-Dimensional Instabilities of an Elastic Plate in a Duct with Compressible Flow. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2018, 78 (6), pp.3119-3144. ⟨10.1137/18M1165761⟩. ⟨hal-02381057⟩

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