考虑稳定性的非线性刚度转子系统振幅突变分叉集分析

摘要

With help of averaging method,a main resonance frequency response equation of a nonlinear stiffness rotor system was derived.Expressions of bifurcation set and its cusp were obtained based on catastrophe theory,which were represented by frequency coordination factor and excitation force amplitude.Stability conditions of a rotor system were derived based on stability theory of singular points,and expressions of critical unstable regions and its bifurcation points were also given by frequency coordination factor and amplitude.Influences of nonlinear stiffness on bifurcation catastrophe areas,unstable regions and amplitude characteristic curves were discussed though numerical examples.The results show that reducing nonlinear stiffness values is the best method to control amplitude catastrophe of the rotor systems.%利用平均法导出非线性刚度转子系统的主共振频率响应方程,借助突变理论求出利用频率协调因子和激振力幅值表示的分叉集及其尖点表达式.根据奇点稳定性理论导出了转子系统稳定性条件,并得到利用频率协调因子和振幅构建的临界不稳定区域及其分叉点表达式.利用数值算例讨论了非线性刚度系数对分叉集突变区域、临界不稳定区域以及振幅特性曲线的影响.研究表明:减小转子系统的非线性刚度系数是控制转子系统振幅突变最为理想的方法.