# Study on Coupled Vertical Vehicle-Bridge Dynamic Performance of Medium and Low-Speed Maglev Train
## 1 Introduction  
Medium and low-speed maglev trains have been gradually introduced in cities due to their advantages of strong climbing ability, small turning radius, and low noise. At present, four commercial operation lines of medium and low-speed maglev trains have been built in the world, which are distributed across Japan, South Korea, and Changsha and Beijing in China. Different from the traditional wheel-rail train operation mode, a certain gap is maintained between the train and the track so that maglev trains are not limited by sliding friction [1; 2; 3]. Through electromagnetic induction between the electromagnet on the vehicle suspension frame and the coil reaction plate on the track, a generated levitation force is generated to levitate the maglev train. In the process of operation, the loss of train stability or collision of rail will occur due to uneven load of vehicle or track irregularity. Therefore, it is of great significance to study the dynamic performance of the coupled vehicle-bridge system for the smooth operation of maglev trains. Elevated guideways are widely applied in maglev systems. Compared with the traditional wheel-rail train, bridges are also an important part of maglev systems in addition to the track and vehicle. Therefore, the train-track-bridge system is used as a researchobject in many studies. [PERSON]. [PERSON] et al. [4] proposed a vertical dynamic interaction model of medium and low-speed maglev train-track-bridge system and discussed the vibration characteristics of F-type track and the influence mechanism of track structure on the dynamic bridge response. [PERSON] et al. [5] developed a vertical coupling vibration simulation program for maglev vehicles and simply supported beam system, compared the simulation results with the dynamic response of field test. [PERSON]. [6] and [PERSON]. [7] carried out the dynamic test of the train-track-bridge system for the new suspension bogie with a central air spring. [PERSON]. [PERSON] et al. [8] established a dynamic coupling model of medium and low-speed maglev vehicle-controller-bridge systems and studied the vertical dynamic response of vehicle and bridge when trains run at different speeds and different vehicle loads. [PERSON] et al. [9] established coupled vehicle-bridge dynamic model to analyze the vibration response characteristics in the floating stage. [PERSON] et al. [10] integrated a three-dimensional vehicle model, multi-modality guideway model, and feedback suspension control algorithm to study the dynamic characteristics of vehicles and rail at low speed. As an important infrastructure of the maglev line, the characteristics of the bridge itself were closely related to vehicle-bridge coupling vibration performance [11,12]. [PERSON] et al. [13] studied the dynamic interaction between medium and low-speed maglev trains and bridges with different vertical deflection ratios and proposed the allowable deflection ratios for bridges with different spans. [PERSON] et al. [14] analyzed the vertical dynamic characteristics and vertical resonance mechanism of maglev train-bridge systems with different beam heights. [PERSON]. [15] proposed the limit values of key design parameters, including dynamic coefficient, natural frequency, vertical stiffness, transverse stiffness, and bending angle of beam end, suitable for medium and low-speed maglev operation. [PERSON]. [PERSON] et al. [16] studied the vibration effects of a simply supported beam and continuous beam on vehicles and bridges. [PERSON] [17] established the dynamic control equation of coupled vehicle-guideway model and controller and studied the dynamic performance of vehicle speed, deflection ratio, span length, span continuity, and damping ratio. At present, there are many studies on the dynamic performance of the vehicle-track coupling system. On the one hand, numerical simulations are carried out by establishing the vehicle-track coupling model combined with the controller, and the dynamic response of the system with various influencing factors is analyzed.