Abstract
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t → ∞.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barbu, V. Nonlinear semigroups and differential equations in Banach spaces. Nordhoff, International Publishing, Bucuresti, România, 1976
Feng, D.X., Zhang, W.T. Nonlinear feedback control of Timoshenko beam. Science in China (Series A), 38:918–927 (1995)
Liu, K.S., Liu, Z.Y. Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping. SIAM J. Control and Optimization, 36:1086–1098 (1998)
Yan, Q.X. Boundary stabilization of Timoshenko beam. Systems Science and Mathematical Sciences, 13(4):376–384 (2000)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China(Grant No. 60174008).
Rights and permissions
About this article
Cite this article
Yan, Qx., Zou, Hc. & Feng, Dx. Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam. Acta Mathematicae Applicatae Sinica, English Series 19, 239–246 (2003). https://doi.org/10.1007/s10255-003-0099-x
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10255-003-0099-x
Keywords
- Timoshenko beam
- boundary feedback stabilization
- nonlinear semigroups
- exponential multiplier
- energy perturbed method