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Journal of Applied Nonlinear Dynamics 4(3) (2015) 229--237 | DOI:10.5890/JAND.2015.09.003

Zhao-Hui Ren$^{1}$, Yu-Hang Xu$^{1}$, Yan-Long Han$^{2}$, Nan Zhang$^{1}$, Bang-Chun Wen$^{1}$

$^{1}$ School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110004, China

$^{2}$ Department of Mechanical Engineering, Chengde Petroleum College, Chengde 067000, China

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Abstract

Self-synchronization, compound synchronization and intelligent control synchronization widely exist in the mechanical system engineering, while lag self-synchronization movement is a special form of cooperation movement. Based on coupling Duffing system, this paper studies lag self-synchronization problem, analyses general change law of the system co-rotating synchronization frequency, antisynchronization frequency and lag phase angle by analytic analysis and numerical quantitative analysis, studies coupling parameter influences on systematic lag self-synchronization, and analyses the cause of lag self-synchronization. The results show that the root cause of lag self-synchronization is systematic stiffness namely systematic natural characteristic; that co-rotating synchronization vibration frequency and phase difference depend on coupling stiffness parameter; and that frequency and phase difference of anti-synchronization vibration are independent of coupling stiffness parameter; and when coupling stiffness parameter is larger, phase difference of two oscillators in the two kinds of synchronization is nonzero constant value.

Acknowledgments

The authors gratefully acknowledge the financial support provided by Natural Science Foundation of China (No. 51475084).

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