二自由度车辆垂向振动系统的Hopf分岔  

Hopf Bifurcation of Two-degree-of-freedom Vehicle Vertical Vibration System

作　　者：安金凯 乐源[1] AN Jinkai;YUE Yuan(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都611756

出　　处：《四川轻化工大学学报（自然科学版）》2024年第4期11-18,共8页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11732014)。

摘　　要：建立了一类以空气弹簧拟合的具有高阶非线性项的二自由度车辆垂向振动系统模型,采用非自治系统的多尺度法得到系统的平均化方程,应用数值模拟方法获得分岔点邻域的分岔图及相图,研究了系统在正弦激励下的Hopf分岔。再通过投影法计算分岔点处的第一李雅普诺夫系数并根据其正负判断分岔类型,通过数值模拟方法得到系统的相轨迹图,采用解析法和数值法对Hopf分岔点邻域内的动力学现象进行分析。结果表明:当外激励频率ω和固有频率ω2的接近程度在0.0114附近时系统发生亚临界Hopf分岔,在分岔点的邻域内稳定焦点失稳形成不稳定焦点;当外激励频率ω和固有频率ω2的接近程度在0.0621附近时,系统将发生超临界Hopf分岔,在分岔点邻域内稳定极限环变为稳定焦点。A two-degree-of-freedom vehicle vertical vibration system model with high order nonlinear terms fitted by air spring is established.The average equation of the system is obtained by using the multi-scale method of non-conservative system.The bifurcation diagram and phase diagram of the bifurcation point neighborhood are obtained by numerical simulation,and the Hopf bifurcation of the system under sinusoidal excitation is studied.The first Lyapunov coefficient at the bifurcation point is calculated by projection method and the bifurcation type is judged according to its positivity or negativity.The phase trajectory diagram of the system is obtained by numerical simulation method.The kinetic phenomena in the neighborhood of Hopf bifurcation point are analyzed by analytical method and numerical method.The results show that the subcritical Hopf bifurcation occurs when the external excitation frequency and natural frequency are close to 0.0114,and the stable focus becomes unstable in the neighborhood of the bifurcation point.When the external excitation frequency and natural frequency are close to 0.0621,the system will have a supercritical Hopf bifurcation,and the stable limit cycle becomes a stable focus in the neighborhood of the bifurcation point.

关 键 词：非自治系统 多尺度法 投影法 HOPF分岔 

分 类 号：O313[理学—一般力学与力学基础]