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研究了含有居中盘和悬臂盘的转子轴上出现裂纹时盘的非线性动态响应。在推导出系统的动力学方程的基础上进行了数值求解。由结果可以看出 ,盘的摆振在无裂纹时一般为与转速相同的同频振动 ,一旦裂纹出现 ,摆振一般为转速的倍频运动。裂纹的深度、转子转速、外阻尼和转子不平衡量对盘的非线性响应有很大影响。增大阻尼和不平衡量会抑制混沌运动。系统运动进入混沌的道路主要有 3条 :拟周期进入混沌 ,拟周期经拟周期分叉进入混沌 ,阵发性进入混沌。阵发性混沌过程中随时间变化存在倍周期分叉现象
The nonlinear dynamic response of a disk on a rotor shaft containing a center disk and a cantilever disk was investigated. Based on the derivation of the dynamic equations of the system, the numerical solution is carried out. It can be seen from the results that when the crack of the disk is crack-free, it is generally the same frequency vibration with the same speed, and once the crack occurs, the shimmy is generally multiplied by the rotational speed. The depth of crack, rotor speed, external damping and rotor imbalance have a great influence on the nonlinear response of the disk. Increasing damping and unbalance will suppress chaos. There are three main routes for system movement into chaos: quasi-periodic chaos, quasi-periodic quasi-periodic bifurcation into chaos, and paroxysmal chaos. There are doubling period bifurcations in the process of paroxysmal chaos with time