Crisis and quasiperiod-quasiperiod intermittency in a vibro-impact system

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (7) : 1-7.

YUE Yuan,MIAO Pengcheng

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Abstract

Crisis and quasiperiod-quasiperiod intermittency in a 3-DOF vibro-impact system with symmetry were studied.The system’s 6-dimensional Poincaré map was expressed as the second iteration of another unsymmetric map,it implied that the system has a symmetry.Two conjugate quasi-periodic motions,coming from two conjugate periodic motions after Hopf bifurcation coexisted widely in such a dynamic system.According to the limit set theory of dynamic systems and the symmetry of the limit set,a distance function was introduced to detect the crisis of symmetry increasing.It was shown that when the minimum distance between a pair of conjugate chaotic attractors and an unstable symmetric fixed point is close to zero,a pair of conjugate chaotic attractors do not collide with the unstable symmetric fixed point on the attracting field boundary,to lead to a crisis.Numerical simulations revealed that a new intermittency behavior named the quasiperiod-quasiperiod intermittency occurs; the mechanism of symmetry restoring of quasi-periodic motion is two conjugate tori (quasi-periodic) → doubling of two conjugate tori → two conjugate band chaos attractors → a pair of symmetric chaos attractors → one symmetric torus (quasi-periodic); the symmetric limit set is introduced to distinguish symmetric attractors from conjugate ones; Lyapunov exponent spectrum computed with QR method is used to determine the type of attractors; the quasiperiod-quasiperiod intermittency is of importance for the optimization design of vibro-impact systems.

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vibro-impact system

/ quasi-periodic motion / crisis / intermittency

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YUE Yuan,MIAO Pengcheng. Crisis and quasiperiod-quasiperiod intermittency in a vibro-impact system[J]. Journal of Vibration and Shock, 2017, 36(7): 1-7

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