Abstract
In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω s and ω s = 2ω c ) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.
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Y. S. Hamed received his B.S. degree in Mathematics from Menofia Univer- sity, EGYPT, in 1998. He then received his M.S.c and Ph.D. degrees from Menofia University, in 2005 and 2009, respecttively. Dr. Y. S. Hamed is currently an Assistant Professor of Pure Mathematics at the Department of Engineering Mathematics, Faculty of Electronic Engineering Menofia University, Egypt. Dr. Y. S. Hamed research interests include Differential equations, Numerical Analysis, and Vibration control.
Y. A. Amer received his B.S. degree in Mathematics from Zagazig University, EGYPT, in 1992. He then received his M.S.c and Ph.D. degrees from Zagazig University, in 1996 and 2002, respecttively. Dr. Y. A. Amer is currently an Assistant Professor of Mathematics at the Department of Mathematics, Faculty of Science, Zagaziga University, Egypt. Dr. Y. A. Amer research interests include Non linear dynamical systems, Numerical Analysis, Vibration control, Partial differential equations.
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Hamed, Y.S., Amer, Y.A. Nonlinear saturation controller for vibration supersession of a nonlinear composite beam. J Mech Sci Technol 28, 2987–3002 (2014). https://doi.org/10.1007/s12206-014-0706-1
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DOI: https://doi.org/10.1007/s12206-014-0706-1