非线性共振系统稳态运动方程组的约化

Reduction of Equations of Steady State Motion of Nonlinear Resonance System

非线性共振系统稳态运动方程组是含有三角函数且未知量为模态振幅和共振相位的超越代数方程组 ,并且三角函数前的系数具有对等性 .利用三角关系 sin2 α+cos2 α=1 ,可将非线性共振系统稳态运动方程组约化 。

Equations of steady state motion of the nonlinear resonance system are transcendantal algebric equations which contain trigonometric function unknown quantity of transcendantal algebric equations are modal amplitude and resonance phase,and coefficients of trigonometric equations have equity propenty.Based on the obove characteristics and by using relation of trigonometric function sin 2 α +cos 2 α =1 Equations of steady state motion of the nonlinear oscillation resonance system are simplified and easy to solve and analyze.