三自由度单侧刚性约束振动系统的周期运动和分岔

Periodic Motions and Bifurcations of a Three degree of freedom Vibratory System with a Rigid Constrain

建立了一类具有单侧刚性约束的三自由度冲击振动系统的周期z=1/n运动及Poincaré映射方程,通过分析映射的Jacobian矩阵,从理论上研究了该系统周期运动的稳定性和局部分岔,并通过数值仿真揭示了该系统周期z=1/n运动经内依马克-沙克分岔、倍周期分岔通向混沌的演化过程.

Period n single-impact motions and the Poincare mapping of a three-degree-of-freedom vibratory system with a rigid constrain are derived analytically. Stability and local bifurcations of period n single-impact motions are analyzed theoretically by using Jacobian matrix of the Poincare mapping. It is demonstrated that the system can exhibit chaotic behaviors by Neimark-Sacker bifurcation and doubling-periodic bifurcation of periodic motion. Routes from Neimark-Sacker bifurcation and period doubling bifurcation of periodic motions to chaos are probed by numerical simulations.