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Uniform stabilization of a nonlinear structural acoustic model with a Timoshenko beam interface
Author(s) -
Dalsen Marié GrobbelaarVan
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.737
Subject(s) - nonlinear system , timoshenko beam theory , beam (structure) , mathematics , boundary value problem , partial differential equation , interface (matter) , mathematical analysis , boundary (topology) , stability (learning theory) , classical mechanics , mechanics , physics , computer science , optics , bubble , quantum mechanics , maximum bubble pressure method , machine learning
Abstract This paper is concerned with a nonlinear model which describes the interaction of sound and elastic waves in a two‐dimensional acoustic chamber in which one flat ‘wall’, the interface, is flexible. The composite dynamics of the structural acoustic model is described by the linearized equations for a gas defined on the interior of the chamber and the nonlinear Timoshenko beam equations on the interface. Uniform stability of the energy associated with the interactive system of partial differential equations is achieved by incorporating a nonlinear feedback boundary damping scheme in the equations for the gas and the beam. Copyright © 2006 John Wiley & Sons, Ltd.