扩展方程方法在轴承非线性分叉问题中的应用

Application of Evolution Equations Methods in Solving Nonlinear Bifurcation Problems for Rotor-Bearing System

介07绍了求解非线性自治系统定常解分叉、HOPF分叉问题的扩展方程方法，其基本思想是：根据各种分叉情况的发生条件，对原系统方程适当增加相应的约束方程，从而形成系统动力学特性随某─参数变化时而发生分叉问题的定解条件．文中利用此方法求解了一实际平衡转子─轴承非线性系统随转速变化的单参数族系统的分叉点，结果证明，扩展方程方法在求解转子的半频涡动和油膜荡振方面具有有效的应用价值，能够快速准确地确定转子的失稳转速．

Evoution equation method of solving static state bifurcation 、HOPF bifurcation problems are introduced for nonlinear autonomeus systems. Its basic ideas are that: the corrponding determining soution conditions for the mentioned bifurcation problems are formed by adding constained equations to the original system equation . Using the methods the bifurcation points of an actual balanced rotor-bearing system which vary with rotating speeds are ob-tained. The results show that the method is very effective in studying subharmonic vibraion and oil whip, and it can rapidly determine the instability points.