一类滞后相对转动动力学方程的分岔特性及其解析近似解

The bifurcation of a kind of relative rotational dynamic equation with hysteresis and its approximate solution

建立了一类含Davidenkov滞后环的非线性相对转动动力学方程.分别分析了该非线性相对转动自治方程和微外扰下非自治方程的分岔特性,并采用KBM法求解了滞后环指数n=2时该非线性相对转动方程在周期激励下的解析近似解.通过数值仿真,得到了几种分岔结构及外扰下全局分岔图,同时将数值解与本文KBM法求解结果进行比较,证明本文求解结果有较高的精度,为研究这一类滞后相对转动系统提供了理论参考依据.

Based on the Lagrange function, a new nonlinear relative rotational equation with Davidenkov hysteresis is established. Firstly, the bifurcation characteristics of the hysteretic relative rotational autonomous function and non-antonomous function are discussed. Secondly, the approximate solution of the nonlinear function under periodic force excitation is obtained by KBM method. At last, by numerical simulation, several bifurcation structures are obtained, and the comparisons result indicate the approximate solution of KBM method has higher accuracy and better reflects the dynamic characteristic of equation effectively.