Multi-pulse chaotic dynamics of an unbalanced Jeffcott rotor with gravity effect

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• 作者：Tian-Jun Yu ; Sha Zhou ; Wei Zhang ; Xiao-Dong Yang
• 关键词：Unbalanced Jeffcott rotor ; Localized mode ; Coupled mode ; Chaotic dynamics ; Multi ; pulse orbits ; Šilnikov orbits
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：1
• 页码：647-664
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

In this study, multi-pulse chaotic dynamics of an unbalanced Jeffcott rotor with gravity effect are investigated. Based on the solvability conditions obtained for the case of one-to-one internal resonance and primary resonance, canonical transformations are used to reduce these ordinary differential equations to a standard form suitable for applying the energy-phase method. The global perturbation technique is employed to demonstrate the existence of chaotic dynamics by identifying multi-pulse jumping orbits in the perturbed phase space. The chaotic dynamics results from the existence of Šilnikov’s type of homoclinic orbits and the parameter set for which the system may exhibit chaotic motions in the sense of Smale horseshoes are obtained analytically. The global solutions are then interpreted in terms of the physical motion of the rotor system, and the dynamical mechanism of pattern conversion between the localized mode and the coupled mode is revealed.