振动锤的周期运动稳定性与分叉

通过理论分析和数值仿真,研究了振动锤周期运动的稳定性和局部分叉,得到了n-1周期运动存在的充要条件·应用Poincare映射的分叉理论,揭示了该类冲击振动机械系统存在倍周期分叉·研究表明,当改变恢复系数时,解的周期结构随激振频率的变化有较大的差异·当改变质量比时,解的周期结构没有明显的变化·选择不同的系统参数可以使振动锤工作在不同的周期运动,可以从这些周期运动中选择最为理想的工艺指标和其他综合评价指标最佳的运动形式·所以,研究振动锤的周期性冲击的稳定性与分叉可以使振动锤的系统参数优化·

Stability and Bifurcation of Periodic Motions of Impact Hammer

Stability and partial bifurcation of the impact hammer were investigated through theoretical analysis and numerical simulation to give the necessary and sufficient condition for n-1 periodic impact motion. Based on Poincare mapping bifurcation theory, the existence of a doubled periodic bifurcation is revealed in such impact/shock mechanic systems. It is also indicated that the structure of the periodic solution changes greatly with the change of stimulating frequency if modifying the restoring coefficient. However, no significant structure change of the periodic solution can be found if modifying the mass ratio. So, choosing different system parameters may cause impact hammer to work in different periodic motions among which one can be picked out as the most appropriate technological index with the other one as the best index for overall evaluation. The study on the stability and bifurcation of periodic motions can therefore provide a theoretical basis for the optimal dynamic design of impact hammers.