On a structural acoustic model with interface a Reissner-Mindlin plate or a Timoshenko beam

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:320

Article

Grobbelaar-Van Dalsen, Marie

关键词: structural acoustic model;    Reissner-Mindlin plate;    Timoshenko beam;    uniform stabilization;   

DOI  :  10.1016/j.jmaa.2005.06.034

来源: Elsevier

【 摘 要 】

This paper is concerned with a model which describes the interaction of sound and elastic waves in a structural acoustic chamber in which one wall is flexible and flat. The model is new in the sense that the composite dynamics of the three-dimensional structure is described by the linearized equations for a gas defined on the interior of the chamber and the Reissner-Mindlin plate equations on the two-dimensional flat wall of the chamber, while, if a two-dimensional acoustic chamber is considered, the Timoshenko beam equations describe the deflections of the one-dimensional wall. With a view to achieving uniform stabilization of the structure linear feedback boundary damping is incorporated in the model, viz. in the wave equation for the gas and in the system of equations for the vibrations of the elastic medium. We present the uniform stability result for the case of a two-dimensional chamber and outline the method for the three-dimensional model which shows strong resemblance with the system of dynamic plane elasticity. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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