含干摩擦及非线性约束碰撞系统的动力学特性

DYNAMIC CHARACTERISTICS OF A COLLISION SYSTEM WITH DRY FRICTION AND NONLINEAR CONSTRAINTS

研究了一类单自由度含干摩擦及非线性约束机械碰撞振动系统,通过四阶变步长Runge-Kutta数值算法,分析了该机械振动系统在低频激励下产生的p/1周期运动的动力学特性及其转迁规律,采用多参数协同仿真的方法分析了系统参数对该振动模型动力学特性的影响,揭示了Grazing分岔和Saddle-node在p/1周期运动中的频率迟滞特性以及共存吸引子的范围。最后,结合胞映射法研究了多态共存区内不同吸引子及吸引域的分布情况及其转迁规律。研究结果表明,随着激振频率的减小,Grazing分岔会使p/1周期运动的碰撞次数逐步增加直至发生颤碰运动,而且由于相邻周期运动的不可逆性,在迟滞域内改变不同的初值会得到不同的周期运动共存。

A type of single-degree-of-freedom mechanical impact vibration system with dry friction and nonlinear constraints is studied.Through the fourth-order variable step Runge-Kutta numerical algorithm,the dynamics of the mechanical vibration system generated by the low-frequency excitation of the p/1 periodic motion are analyzed.The effect of system parameters on the dynamic characteristics of the vibration model is analyzed by the method of multi-parameter co-simulation,and the frequency hysteresis characteristics of Grazing bifurcation and Saddle-node in p/1 periodic motion are revealed.And the range of coexistence attractors.Finally,combined with the cell mapping method,the distribution of different attractors and attracting domains in the polymorphic coexistence area and their transition laws are studied.The research results show that the Grazing bifurcation with the decrease of the excitation frequency,the number of collisions of the p/1 periodic motion will gradually increase until the flutter motion occurs,and due to the irreversibility of adjacent periodic motion,changing different initial values in the hysteresis domain will result in different periodic motions coexisting.