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

2008, Volume 3, Issue 4: 723-747. doi: 10.3934/nhm.2008.3.723

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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.
- Star-shaped network,
- Euler-Bernoulli beam,
- asymptotic stability,
- subspace Riesz basis
Citation: Gen Qi Xu, Siu Pang Yung. Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping[J]. Networks and Heterogeneous Media, 2008, 3(4): 723-747. doi: 10.3934/nhm.2008.3.723

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Abstract

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.
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