International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000505

Dynamic Behaviors of an Impact Oscillator in Harmonic Excitation

Jianlian Cheng^1,a, Xinxin Xu^1,b, Yitian Chen² and Bei Xia^{1,c 1}MOE Key Laboratory for Highway Construction Technology and Equipment,
Department of Mechanical Engineering, Construction Machinery School,
Chang’an University, Xi’an P. R. China. ^acheng19690912@163.com ^bxuxinxin1218@163.com ^cxiabei0820@163.com ²School of Mechatronic Engineering,
China University of Mining and Technology, Xuzhou, P. R. China. chengyt2008@126.com

ABSTRACT

In this paper, stability periodic motions and bifurcation of an impact oscillator is inves- tigated analytically and numerically under a periodic excitation. The initial conditions of theoretical solution of unsymmetrical periodic-1 impact motion are obtained by dif- ferential equations. The Poincaré map of impact system is established. The analytical predictions of periodic motions are based on the mapping structures. The stability and bifurcation conditions for symmetrical and unsymmetrical periodic motions are given analytically. The numerical prediction of special unsymmetrical motions is completed. The theoretical analyses are verified by numerical solutions. The strange attractors of the chaotic motion induced by period doubling are presented by use of phase planes and the Poincaré mapping sections. The results show that dynamical behaviors of the impact oscillator in the resonance case are more complicated than that of the non-resonance cases.

Keywords: Impact oscillator, Periodic motion, Bifurcation, Chaotic motion.

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