Dynamics of a vibro-impact system by the global analysis method in parameter-state space. (English) Zbl 1430.34054
Summary: The global analysis method in parameter-state space for achieving both the distribution and the transition rule of periodic motions and the distribution rule of the multiple motions coexistence of the vibro-impact system is developed. A nonlinear dynamic model in a system of vibro-impact with asymmetric clearances is researched by the new method. Three grazing motions and relevant conditions have been discussed. The distribution and the transition rule of periodic motions are analyzed. The influence of the grazing and saddle-node bifurcation during the change in the left and the right gaps are demonstrated. The distribution of subharmonic motions is illustrated. The coexistence of multiple motions which exist at the junction of periodic motions within the motion-sensitive areas is researched by the global analysis method in parameter-state space, and the distributions of periodic motions and the multiple motions coexistence are illustrated. The transition of the multiple motions coexistence with the guide of the global distribution of the motions is further analyzed by the evolution of the attractors and the corresponding attracting domains. The results contribute a lot to the study of the transition and the control of the motions.
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 37G10 | Bifurcations of singular points in dynamical systems |
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