一类两自由度碰撞振动系统的分岔与混沌演化

建立了一类两自由度含间隙双边刚性约束机械碰撞振动系统的力学模型。通过理论分析和数值仿真相结合的方法,研究了该系统在适当参数下发生周期倍化分岔和杈式分岔的动力学行为。即在两参数平面上,用运四级四阶变步长Runge-Kutta法和Poincaré映射方法对系统进行数值模拟仿真,分析了当系统参数变化时该类机械系统经周期倍化分岔、杈式分岔向混沌的演化路径,并且揭示了系统主要参数对碰撞振动系统全局分岔的影响,为实际应用中两自由度碰撞振动系统的动力学优化设计提供了理论参考。

Bifurcation and routes to chaos in a two-degree-of-freedom vibro-impact system

A two-degree-of-freedom vibro-impact mechanical system with clearance and doubling piece rigid constraint is considered in this paper.By theoretical analysis and numerical simulation,the dynamical behavior of period-doubling bifurcation and pitchfork bifurcation are investigated in suitable parameter.On the two-parameter plane,the system was numerical simulated by using fourth-band and fourth-order Runge-Kutta algorithm and Poincaré mapping algorithm.As controlling parameter varies further,the routes from periodic motion to chaos via period-doubling bifuracation and pitchfork bifurcation are investigated in this mechanical system.It shows the influence of vibro-impact system by the system major parameter and provide theoretical reference for two-degree-of-freedom vibro-impact system dynamics optimization in the actual application.