滑动轴承不平衡弹性转子系统周期运动的稳定性

利用快速Galerkin方法，结合Floquet理论，在较大的参数范围内研究了滑动轴承不平衡弹性转子系统周期运动的稳定性并进行了数值模拟。研究发现，考虑转子弹性后，较小的不平衡量使得转子刚性较大的系统Hopf分岔提前，而使得转子刚性较小的系统Hopf分岔滞后。系统刚性不同使得倍周期分岔形状发生了很大的变化，从而使得系统在参数空间的失稳途径不同。在较小的不平衡量范围内，随着转速的增大，转子刚性较大的系统失稳方式有两种，而转子刚性较小的系统失稳方式只有其中一种。在较大的不平衡量的范围内，无论转子刚性大小，系统失稳方式相同。

On the Stability of Periodic Motion of an Unbalanced ElasticRotor System Supported on Lubricated Bearings

The stability of the periodic motion of unbalanced elastic rotor systems with oil film bearings is studied by the fast Galerkin method and Floquet theory in a relativelg wide range of parameters At the same time,numerical simulation is carried out and agreeable conclusions are got The study shows that the critical speed of Hopf bifurcation of the systems decreases when the rotor has quite good rigidity and increases when the rotor has a relatively poor rigidity for a better balance rotor The elasticity of the rotor has great effects on the shape of double period bifurcation sets,and different elasticitiesy of rotor have the stability area of the systems in parameter space changed completely When the rotor has fairly good rigidity the system has two kinds of dispersing way for the better balance rotor,whereas only one of them for the rotor with relatively poor rigidity When the rotor is balanced not so well,the systems have the same way to disperse