# American Institute of Mathematical Sciences

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

 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.
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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