# Study on Coupled Vertical Vehicle-Bridge Dynamic Performance of Medium and Low-Speed Maglev Train
## 3 Numerical Simulations  
During the operation of maglev trains, the change of passenger capacity leads to a change in train load. As a key variable of maglev systems, load affects the overall dynamic performance of the system. In addition, the high cost of bridge construction in maglev systems has always been a disadvantage. As a key parameter of the bridge, the stiffness largely determines the cost. Therefore, it is necessary to study how bridge stiffness affects the dynamic response of the system, so as to pave the way for judging the lower limit of the bridge stiffness on the premise of stable operation. The influence of bridge characteristics and vehicle load on the vehicle-bridge coupling vibration system was studied through numerical analysis on the Matlab/Simulink platform. The physical parameters of the coupled maglev vehicle-bridge system are shown in Table 1. In order to form mutual verification with the field test, the real parameters of a maglev train were used for the simulation analysis. In order to analyze the influence of vehicle load \(M\) on vehicle-bridge coupling vibration, the dynamic system response under no load \(M=33\) t and overload \(M=39\) t was analyzed, respectively. It can be seen from Figure 3a-d that the airgap, bridge deflection, acceleration of electromagnet, and bridge tended to be stable, which indicates that the stable suspension could be maintained no matter if there is no load or an overloaded mass. Comparing the dynamic response changes under different loads, it can be seen in Figure 3a that during 1-3 s the response speed of the gap was decreased due to the increase in load. In order to adjust the gap dynamically, the levitation force was increased to balance with gravity, but the real-time change of levitation force was weakened. Therefore, as shown in Figure 3c,d, the vertical acceleration of electromagnet and bridge increased. In addition, in Figure 3b, the static deflection of the mid-span bridge was about 0.545 mm under no-load conditions, and it was about 0.642 mm when overloaded, with an increase of 0.097 mm. In the field test, the stiffness of a bridge is usually changed by adjusting beam height. The change of beam height can be regarded as the change of bridge quality. Therefore, at full stiffness, the mass of the steel beam \(m_{r}\) was defined as 50 tons, and the section inertia \(I_{r}\) was 0.9341. After reducing the stiffness (low stiffness), the mass of the steel beam was 45 tons, and the section inertia was 0.7081. The dynamic response of the system under different stiffness is shown in Figure 4.  
The response difference of low stiffness compared with full stiffness shows that the fluctuation amplitude of the gap was larger, as shown in the subgraph of Figure 4a, but there was no significant difference in response speed. In Figure 4b, the mid-span static deflection of the bridge was 0.545 mm at full stiffness and 0.719 mm at low stiffness, with an increase of 0.174 mm. It can be seen from Figure 4c,d that the vertical vibration of the electromagnet and bridge increased due to the decrease in stiffness. Through the simulation analysis, it could be concluded that the increase in load or the decrease in stiffness would have a negative impact on the suspension stability and riding comfort of maglev trains. It indicates that bridge characteristics and vehicle load have a significant influence on the dynamic response of coupled vehicle-bridge systems, which are the important factors to study the vertical dynamic performance of the system.