Abstract:The objective of this study was to reduce vibration by the saturation control. Nonlinear beam dynamic model was established by using Hamilton’s principle of minimum potential energy principle. The frequency responding equation of nonlinear beam was solved with the multi-scale method. The nonlinear beam was saturated by adjusting the effective parameters. The vibration of the nonlinear beam was thus suppressed effectively.
[1] Nayfeh A. H, Mook D. T, and Marshall, L. R. Nonlinear coupling of pitch and roll modes in ship motion[J]. Journal of Hydronautics, 1973, 7:145–152.
[2] P.F.Pai B.Wen, A.S. Naser, M.J. Schulz. Structural vibration control using PZT patches and nonlinear phenomena[J]. Sound Vibration, 1998, 215: 273–296.
[3] S.S. Oueini, A.H. Nayfeh. Analysis and application of a non-linear vibration absorber[J]. Vibration Control and shock, 2000,6:999–1016.
[4] M. Eissa, M. Sayed. Vibration reduction of a three DOF non-linear spring pendulum[J]. Commun Nonlinear, 2008, 13:465–488.
[5] M. Sayed. Improving the Mathematical Solutions of Nonlinear Differential Equations using Different Control Methods, Ph. D. Thesis, Menofia University Egypt, 2006,9.
[6] Banerjee B, Bajaj A K, and Davies P. Second order averaging study of an autoparametric system[J]. In Nonlinear Vibrations ASME, New York, 1993:127–138.
[7] M. Eissa, S. El-Serafi, R. Abd-El-Moniem. Vibration reduction via 1:2 internal resonance active absorber. Sci Bull Fac. Eng Ain-Shams Univ. 2006, 41(3):971–986.