Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback. (26th May 2018)

• Record Type: Journal Article
• Authors: Do, K.D.
• Is Part Of: Journal of sound and vibration. Volume 422(2018)
• Page Start: 278
• Page End: 299
• Publication Date: 2018-05-26
• Subjects: Timoshenko beams -- Three dimensions -- Large motions -- Boundary control -- Hilbert space -- Evolution system; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2018.02.005
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.