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

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Abstract

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.

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Acknowledgments

This research is supported by National Natural Science Foundation of China (NNSFC) through Grant Nos. 11322214, 11672007, 11290152 and 11402028, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB).

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Authors and Affiliations

  1. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Tian-Jun Yu, Sha Zhou, Wei Zhang & Xiao-Dong Yang

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  1. Tian-Jun Yu
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  2. Sha Zhou
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  3. Wei Zhang
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  4. Xiao-Dong Yang
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Correspondence to Xiao-Dong Yang.

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Yu, TJ., Zhou, S., Zhang, W. et al. Multi-pulse chaotic dynamics of an unbalanced Jeffcott rotor with gravity effect. Nonlinear Dyn 87, 647–664 (2017). https://doi.org/10.1007/s11071-016-3066-9

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  • DOI: https://doi.org/10.1007/s11071-016-3066-9

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