Journal of Beijing University of Posts and Telecommunications

  • EI核心期刊

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2007, Vol. 30 ›› Issue (3): 126-133.doi: 10.13190/jbupt.200703.126.zhoucl

• Reports • Previous Articles    

On the Well-Posedness and Stability of an Euler-Bernoulli Beam Under a Special Boundary Feedback

ZHOU Cui-lian1,2, CHANG Jin-de3   


  1. 1. Department of Applied Mathematics, Beijing institute of Technology, Beijing 100081 China;
    2. School of Mathematics and Information Sciences , Shandong University of Technology, Zibo 255049 Shandong China;
    3. Institute of System Sciences, Academy of Mathematics and System Sciences, Graduate School of the Chinese Academy of sciences, Academia Sinica, Beijing 100080 China.
  • Received:2006-09-21 Revised:2006-11-28 Online:2007-06-30 Published:2007-06-30
  • Contact: ZHOU Cui-lian

Abstract:

An Euler-Bernoulli beam equation subject to a special boundary feedback problem is considered. This problem is in sharp contrast to the general principle in engineering practice that the conjugate variables cannot be assigned simultaneously at the same boundary. The Riesz basis approach is adopted in investigation. It is shown that the closed-loop system is well-posed in the usual energy state space and the trajectory approaches to the zero eigenspace of the system as time goes to infinity. Therelease of the engineering restriction gives more freedom in the design of boundary controls for thesuppression of vibration of flexible structures.

Key words: Riesz basis, Euler-Bernoulli beam, boundary control, stability