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Networks and Heterogeneous Media

2008, Volume 3, Issue 4: 723-747. doi: 10.3934/nhm.2008.3.723
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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
  • 2.
    Department of Mathematics, The University of Hong Kong, Hong Kong
  • Received: 01 February 2008 Revised: 01 July 2008

  • Primary: 35B40, 35C10; Secondary: 93D20, 94C99

  • 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[J]. Networks and Heterogeneous Media, 2008, 3(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.


  • This article has been cited by:

    1. Kuiting Zhang, 2014, Stabilization of a triangle network of Euler-Bernoulli Beams, 978-9-8815-6387-3, 6142, 10.1109/ChiCC.2014.6895995
    2. Kuiting Zhang, Genqi Xu, A pinned network of Euler-Bernoulli beams under feedback controls, 2013, 26, 1009-6124, 313, 10.1007/s11424-013-0068-2
    3. Zhong-Jie Han, Gen-Qi Xu, Exponential stabilisation of a simple tree-shaped network of Timoshenko beams system, 2010, 83, 0020-7179, 1485, 10.1080/00207179.2010.481767
    4. Zhong-Jie Han, Gen-Qi Xu, Stabilization and SDG condition of serially connected vibrating strings system with discontinuous displacement, 2012, 14, 15618625, 95, 10.1002/asjc.218
    5. YAN NI GUO, GEN QI XU, EXPONENTIAL STABILISATION OF A TREE-SHAPED NETWORK OF STRINGS WITH VARIABLE COEFFICIENTS, 2011, 53, 0017-0895, 481, 10.1017/S0017089511000085
    6. Hai-E. Zhang, Gen-Qi Xu, Hao Chen, Min Li, Stability of a Variable Coefficient Star-Shaped Network with Distributed Delay, 2022, 35, 1009-6124, 2077, 10.1007/s11424-022-1157-x
    7. Yanni Guo, Yunlan Chen, Genqi Xu, Yaxuan Zhang, Exponential stabilization of variable coefficient wave equations in a generic tree with small time-delays in the nodal feedbacks, 2012, 395, 0022247X, 727, 10.1016/j.jmaa.2012.05.079
    8. A. Kawano, A. Morassi, Load identification in a plate-beam lattice from interior dynamic data, 2024, 125, 0307904X, 347, 10.1016/j.apm.2023.08.036
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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