A finite element approximations of a structural acoustic control problem with a Timoshenko beam interface

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Hernandez, Erwin¹  Spa, Carlos²  van Caloen, Sophie³ 

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Univ Tecn Federico Santa Maria, Dept Matemat, Santiago, Chile

[3] Catholic Univ Louvain, Boole Polytech Louvain, Louvain, Belgium

关键词: Active vibration control;    Acoustic fluid;    Timoshenko beam;    Error estimates;   

DOI  :  10.1016/j.jmaa.2014.11.051

来源: Elsevier

【 摘 要 】

In this work we introduce and analyze a finite element approximation of an active control problem: the reduction of the vibration in a structural acoustic chamber where one of the walls is an elastic beam. The coupled fluid solid system is subjected to an external harmonic excitation force, the control variable corresponds to the amplitude of the forces applied on the beam, and a distributed sensor is placed in a region of the fluid domain. The problem is considered in the framework of the mathematical theory of optimal control. The beam is modeled by a Tiraoshenko equation and the acoustic fluid is described by the pressure variable. The optimal order of convergence is proved for a finite element approximations using low order piecewise polynomials. Numerical test are included to demonstrate the good performance of the methods considered. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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