Structure change mechanism of the attractor basin in a piecewise-smooth vibro-impact system

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (18) : 141-147.

ZHANG Hui1，DING Wangcai1，LI Xianfeng2

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Abstract

When the stresses of workpieces are eliminated by vibratory stress relief, it is often necessary to make objects vibrate by means of exciters or vibrators.The global dynamics of a kind of vibro-impact system with clearance and preloaded spring was devoted.The coexistence of attractors induced by saddle-node bifurcation, period-doubling bifurcation and boundary-collision bifurcation was focused.The attractor annihilation caused by boundary crisis, basin-boundary metamorphoses, and interior crises was also considered.The cell-to-cell mappings in different Poincaré sections were employed to study the co-existence of attractors and their basins of attraction.The results show that the boundaries of basins of attraction are becoming fractal along with the appearance of the regular saddle points induced by grazing bifurcation and the flipped saddle points induced by period-doubling bifurcation.

Key words

Non-smooth dynamical systems / Global analysis；Fractal basin boundary / Cell-to-cell mapping;

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ZHANG Hui1，DING Wangcai1，LI Xianfeng2. Structure change mechanism of the attractor basin in a piecewise-smooth vibro-impact system[J]. Journal of Vibration and Shock, 2019, 38(18): 141-147

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