# Study on Coupled Vertical Vehicle-Bridge Dynamic Performance of Medium and Low-Speed Maglev Train
## 5 Conclusions  
Based on the characteristics of the elastic beam, coupled maglev vehicle-bridge model based on an elastic beam was established, and the rationality of levitation operation under special conditions of overload or low bridge stiffness was verified by a numerical simulation. In addition, the dynamic performance test of a coupled vehicle-bridge system based on steel beam under different stiffness and load conditions was carried out. According to the test data, the levitation gap, vertical deflection of the bridge, vertical vibration characteristics of suspension bogie and the bridge were analyzed using the time and frequency domains, respectively. The main conclusions are as follows:  
1. The levitation gap was significantly affected by the change of load and stiffness. When the load increased, or the stiffness decreased, the response speed of the gap became slower, and there was a steady-state error of about 1 mm under overloaded conditions;
2. Based on the test analysis of various conditions, the deflection of the bridge varied from 2.41 mm to 3.59 mm. At full stiffness, the load increased by 6 tons, and the deflection increased by 1.18 mm. Under no load, the beam height decreased by 20 cm, and the deflection increased by 0.94 mm;
3. The vertical vibration of suspension bogie and bridge increased with an increase in load or decrease in stiffness. At full stiffness, the load increased by 6 tons, and the maximum vertical acceleration of the suspension bogie and bridge increased by 7.25 m/s\({}^{2}\) (87.6%) and 0.401 m/s\({}^{2}\) (51.7%), respectively. Under no-load conditions, the beam height decreased by 20 cm, and the maximum vertical acceleration of suspension bogie and bridge increased by 6.92 m/s\({}^{2}\) (92.3%) and 0.252 m/s\({}^{2}\) (33.9%), respectively. The dynamic response of the suspension bogie changed more obviously;
4. The load had no effect on the first natural frequency of the bridge (about 7.1 Hz) or the suspension bogie (about 5 Hz). However, the stiffness had little influence on the first natural frequency of the bridge, and the low stiffness reduced by 0.6 Hz than the full stiffness and had no effect on the suspension bogie;
5. The frequency band of bridge vibration was in the range of 200 Hz, and that of suspension bogie was in the range of 400 Hz. The vertical vibration of the suspension bogie had more high-frequency components. In addition to the first-order vibration frequency, other frequencies with high energy were mostly caused by forced vibration. However, electromagnetic interference was more serious at 50 Hz and multiple frequencies (power frequency signal);
6. The time-domain law above was consistent with the simulation result, which verifies the reliability of the system model. In addition, the test results could be used as a reference for the design of rail transit coupling systems. In the future, new levitation control algorithms will be applied to the field test to evaluate the dynamic performance under the above conditions so as to further overcome the problems of system stability degradation caused by stiffness reduction or load increase.  
Conceptualization, G.L.; methodology, G.L. and F.N.; software, C.C. and Y.S.; validation, G.L., J.X. and C.C.; formal analysis, Y.S., J.X. and F.N.; investigation, G.L. and J.X.; resources, G.L., J.X. and F.N.; data curation, Y.S. and C.C.; writing--original draft preparation, Y.S.; writing--review and editing, G.L., C.C. and F.N.; visualization, F.N. and Y.S.; supervision, G.L. and J.X.; project administration, G.L. and J.X.; funding acquisition, G.L. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the key special project of advanced rail transit in the 13 th five-year plan \"Research on Key Technologies of medium speed maglev\": 2016 YFB1200601, and the general project of National Natural Science Foundation of China: 52072269.  
Not applicable.