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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :131-138    DOI: 10.1007/s10255-012-0129-7
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Stabilization of Nonuniform Euler-Bernoulli Beam with Locally Distributed Feedbacks
Xian-bing CAO1, Qing-xu YAN2
1. Department of Mathematics, School of Sciences, Beijing Technology and Business University, Beijing 100048, China;
2. Information Engineering School, China Geosciences University, Beijing 100083, China
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Abstract In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.  
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Keywordsnonuniform Euler-Bernoulli beam   linear locally distributed feedback control   linear semigroup   exponential stability   piecewise multiplier method     
Abstract: In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.  
Keywordsnonuniform Euler-Bernoulli beam,   linear locally distributed feedback control,   linear semigroup,   exponential stability,   piecewise multiplier method     
Received: 2009-10-17;
Fund:

Supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (No. 201102) and Beijing Natural Science Foundation (No. 1052007).

Cite this article:   
.Stabilization of Nonuniform Euler-Bernoulli Beam with Locally Distributed Feedbacks[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 131-138
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0129-7      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/131
 
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