Maglev trains are strongly nonlinear, open-loop unstable, and flexible track systems. Vehicle-guideway self-excited vibration, which occurs mainly due to the deflection of the flexible guideway, may take place when a train is levitated on the guideway, even if the train is stationary. In this research, maglev vehicle-guideway coupling vibration is studied by employing the Hopf bifurcation criterion. First, the nonlinear dynamic model is presented with consideration of the flexibility of the guideway. To avoid the massive computations required to solve all the eigenvalues when analyzing system stability, the stability criterion of the Hopf bifurcation for the maglev system is proposed and proven with strict mathematical analysis. Based on the proposed lemma, the bifurcation points of the maglev system are calculated, and the critical points of the coupling vibration are found. Next, the influence law of the parameters of the guideway on the vehicle-guideway coupling vibration is analyzed with theoretical and numerical simulation. Then the influence law and the system stability range of the control parameters are analyzed to suppress the coupled vibration. Finally, the effectiveness of the proposed theory is verified by experiments.

磁悬浮列车是强非线性、开环不稳定和柔性轨道系统。车辆-导轨自激振动主要是由于柔性导轨的挠度引起的，当列车悬浮在导轨上时，即使列车是静止的，也可能发生车辆-导轨自激振动。本研究采用Hopf分岔判据对磁悬浮车辆-导轨耦合振动进行研究。首先，提出了考虑导轨柔性的非线性动力学模型。为避免分析系统稳定性时求解所有特征值所需的大量计算，提出了磁悬浮系统Hopf分岔的稳定性判据，并通过严格的数学分析证明。基于所提出的引理，计算磁悬浮系统的分叉点，并找到耦合振动的临界点。其次,通过理论和数值仿真分析了导轨参数对车-导轨耦合振动的影响规律。然后分析控制参数的影响规律和系统稳定范围以抑制耦合振动。最后，通过实验验证了所提理论的有效性。