一类谐波激励相对转动非线性动力系统的稳定性与近似解

Stability and approximate solution of a relative-rotation nonlinear dynamical system under harmonic excitation

建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程.对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性.运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性.

The dynamical equation of a relative-rotation nonlinear dynamical system with nonlinear elastic force and common friction and harmonic excitation is deduced.The singularity stability of the autonomous system is studied by constructing the Lyapunov function.The approximate solution of unautonomous equation with different resonance response under harmonic excitation is obtained by the method of multiple scales,and the stability of main resonance stable state of motion is studied.