一类含时变间隙的强非线性相对转动系统分岔和混沌

Bifurcation and chaos of some strongly nonlinear relative rotation system with time-varying clearance

建立一类具有时变间隙的两质量相对转动系统的强非线性动力学方程.应用MLP方法求解出变换参数,并运用多尺度法求解该系统发生1/2亚谐共振时的分岔响应方程,采用奇异性理论分析得到系统稳态响应的转迁集,并且得到系统在非自治情形下的分岔特性以及系统的分岔形态.最后通过数值仿真得到系统在间隙和阻尼参数变化下的分岔和混沌行为,发现随着系统参数变化系统将出现周期运动、倍周期运动以及混沌等多种不同的运动形态.

The dynamic equation for the relative rotation nonlinear dynamic system with time-varying clearance is investigated. Firstly, transformation parameter is deduced by using the method of MLP; the bifurcation response equations of 1/2 harmonic resonance then are generated by the method of multiple scales, while singularity analysis is employed to obtain the transition set of steady motion; further more the bifurcation characteristic and the bifurcation of the system under the situation of non-autonomy are analyzed. Finally, numerical simulation exhibits many different motions, such as periodic motion, period-doubling motion, and chaos. It is shown that the change of clearance and damp parameters may influence the motion state of the system.