四川轻化工大学学报（自然科学版）2024，Vol.37Issue(4)：11-18,8.DOI:10.11863/j.suse.2024.04.02
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
摘要
Abstract
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Key words
non-conservative system/multi-scale method/projection method/Hopf bifurcation分类
数理科学引用本文复制引用
安金凯,乐源..二自由度车辆垂向振动系统的Hopf分岔[J].四川轻化工大学学报（自然科学版）,2024,37(4):11-18,8.基金项目
国家自然科学基金项目(11732014) （11732014）
