多重共振系统稳态运动及其稳定性数值分析方法

The Numerically Analysis Method of Steady State Motion and Its Stability of Multi-Resonances System

提出了多重共振发生的条件,给出了约化后多重共振系统稳态运动方程的形式,并应用牛顿下山法或梯度法求解约化后多重共振系统稳态运动方程(组)。根据多重共振系统稳态运动解的稳定性判定定理和对应的雅克比矩阵的特点,采用求解一般实矩阵全部特征值的QR方法判断多重共振系统稳态运动解的稳定性,并给出了应用实例。

The conditions of multi-resonances are given and so are equations of simplified steady state motion of multi-resonances..By means of Newton Method and or Gradient Method,equations of steady state of multi-resonances system can be solved.QR Method is used to judge stability of steady state solutions and characteristics of corresponding Jacobian Matrix with practical examples.