# Study on Coupled Vertical Vehicle-Bridge Dynamic Performance of Medium and Low-Speed Maglev Train
## 4 Test Results and Analysis
### Parametric Analysis
#### 4.2.2 Bridge Stiffness  
Under the premise of consistent vehicle load, the change of bridge stiffness directly affected the deflection of the bridge. As shown in Figure 12a, the initial vertical displacement was set as 42 mm. The average deflection of the bridge was 38.64 mm at low stiffness and 39.58 mm at full stiffness. In this test, the bridge stiffness was changed by changing beam height. The decrease in beam height led to a decrease in section inertia. According to Equation (19), there is an inverse relationship between the section inertia and the static deflection of a bridge; thus, the reduction in stiffness would increase the mid-span deflection (about 0.94 mm), which was also reflected in the numerical results in Figure 4b. Due to the dynamic change of levitation force during static levitation, the vertical deflection of bridge changes in real-time under the influence of levitation force; as shown in Figure 12b, the fluctuation bandwidth of bridge deflection was wider when the stiffness was low. In the levitation process of the test train, the time-domain vibration waveform of the bridge was composed of forced vibration caused by floating (or landing) and free vibration after stable levitation. The first natural frequency of the bridge could be determined using a Fourier transform of the vibration waveform. As shown in Figure 13, the maximum acceleration of full stiffness and low stiffness were 0.743 m/s\({}^{2}\) and 0.995 m/s\({}^{2}\), respectively. It indicates that the decrease in beam height by 20 cm would increase the vertical acceleration  
Figure 11: Effect of load on the vertical deflection of the bridge: (**a**) absolute displacement and (**b**) relative displacement. Figure 12: Effect of stiffness on the vertical displacement of the bridge: (**a**) absolute displacement and (**b**) relative displacement. of the bridge by 0.252 m/s\({}^{2}\), which also verifies the simulation results in Figure 4d. It could be concluded that the decrease in stiffness would increase the vibration amplitude when the bridge is subjected to the same external excitation. As shown in the spectrum diagram, the first natural frequency was 7.965 Hz at full stiffness and 7.324 Hz at low stiffness, which was reduced by 0.6 Hz. Meanwhile, the first-order natural frequency \(f\) in Figure 13 and the conversion value of natural frequency \(\omega\) in Equation (9) meet the relationship: \(f=\omega/L\), where \(L\) represents the span of a bridge [15]. It can be further seen that the frequency band distribution of the bridge in the range of 200 Hz was wide. It could be judged that the high frequency and local vibration of the bridge made the vibration increase in the high-frequency section. In addition, the power spectrum energy of 40-45 Hz was higher, as shown in the subgraph, which indicates that the periodic irregularity caused by the local deformation of the bridge increased the vibration in the low-frequency section. The effect of bridge stiffness on the vertical acceleration of suspension bogie is shown in Figure 14. The maximum vertical acceleration of full stiffness and low stiffness were 7.493 m/s\({}^{2}\) and 14.413 m/s\({}^{2}\), respectively, which is obviously larger than the vibration amplitude of the bridge. It indicates that the vibration acceleration of suspension bogie increased by 6.92 m/s\({}^{2}\) when the bridge height was reduced by 20 cm, and in the 40-60 s stage when the train was suspending, the vibration with low stiffness was significantly greater than that of the full stiffness. It can be seen from the spectrum diagram that the frequency band distribution in the range of 400 Hz was wider, and it had more high-frequency components than the bridge vibration spectrum, which could be regarded as the interference vibration caused by the complex components inside suspension bogie and the connected carriage. The first-order vibration frequency was 4.62 Hz at full stiffness and 5.24 Hz at low stiffness.