Stochastic boundary control design for Timoshenko beams with large motions. (18th August 2017)

• Record Type: Journal Article
• Authors: Do, K.D.
• Is Part Of: Journal of sound and vibration. Volume 402(2017)
• Page Start: 164
• Page End: 184
• Publication Date: 2017-08-18
• Subjects: Timoshenko beams -- Large motion -- Boundary control -- Hilbert space -- Stochastic evolution system; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2017.05.003
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: This paper considers modeling and boundary control of Timoshenko beams with large motions under both deterministic and stochastic external loads. The original nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The control design is based on the Lyapunov direct method. The proposed controllers guarantee globally practically K ∞ -exponentially p -stability of the beam motions at the reference state. Well-posedness and stability are analyzed based on a Lyapunov-type theorem developed to study well-posedness and stability for a class of stochastic evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.