二自由度车辆垂向振动系统的Hopf分岔OA

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.