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December  2008, 3(4): 723-747. doi: 10.3934/nhm.2008.3.723

Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping

Gen Qi Xu 1, and  Siu Pang Yung 2,

1. 

Department of Mathematics, Tianjin University, Tianjin, 300072, China
2. 

Department of Mathematics, The University of Hong Kong, Hong Kong, China

Received  February 2008 Revised  July 2008 Published  October 2008

In this paper we study a star-shaped network of Euler-Bernoulli beams, in which a new geometric condition at the common node is imposed. For the network, we give a method to assert whether or not the system is asymptotically stable. In addition, by spectral analysis of the system operator, we prove that there exists a sequence of its root vectors that forms a Riesz basis with parentheses for the Hilbert state space.
Keywords: asymptotic stability, Star-shaped network, Euler-Bernoulli beam, subspace Riesz basis.
Mathematics Subject Classification: Primary: 35B40, 35C10; Secondary: 93D20, 94C99.
Citation: Gen Qi Xu, Siu Pang Yung. Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping. Networks and Heterogeneous Media, 2008, 3 (4) : 723-747. doi: 10.3934/nhm.2008.3.723
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