Abstract
Grazing bifurcation might bring dramatic and abrupt qualitative changes of system responses in non-smooth systems. The control problem of near-grazing dynamics in a two-degree-of-freedom vibro-impact system with a clearance is addressed in this paper. The discontinuity mapping is built to derive a normal form map near the grazing point. Based on the stability criterion of grazing orbit formulated through the normal form map, a discrete-in-time feedback method is developed to control the stability of grazing orbit in the vibro-impact system. Numerical simulations reveal a discontinuous grazing bifurcation with a jump between the transitions of periodic motions and show the feasibility of the proposed control strategy.
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Acknowledgments
This work was supported by the National Science Fund for Distinguished Young Scholars in China (No. 11225212), the National Natural Science Foundation of China (Nos. 11002052, 11072074, 11372101 and 61364001), the Hunan Provincial Natural Science Foundation for Creative Research Groups of China (Grant No. 12JJ7001), the Young Teacher Development Plan of Hunan University, and the Collaborative Innovation Center of Intelligent New Energy Vehicle.
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Xu, H., Yin, S., Wen, G. et al. Discrete-in-time feedback control of near-grazing dynamics in the two-degree-of-freedom vibro-impact system with a clearance. Nonlinear Dyn 87, 1127–1137 (2017). https://doi.org/10.1007/s11071-016-3103-8
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DOI: https://doi.org/10.1007/s11071-016-3103-8