# Vibration Response Analysis of Overhead System Regarding Train-Track-Bridge Dynamic Interaction
## 4 Conclusions  
In this study, the vertical and horizontal lifting girder overhead system model was created using finite element software, and the corresponding freight and passenger train models and track models were created using the multi-body dynamics software Universal Mechanism. An external flexible body was brought into UM together with the overhead system in order to conduct the train bridge joint simulation. The dynamic reaction of the train track overhead system was investigated by the UM post-processing program. These are the results.  
(1) The analysis concluded that the response of the train body is more sensitive to track irregularity, which mainly affected the safety index of train operation, and that the Sperling index of the train body met the requirements at all levels. When the irregularity level was lower than AAR5, there was a risk of derailment and overturn of the train. For the construction process of this road bridge, the linear change of the track should be strictly controlled to ensure that the smoothness of the track meets the AAR5 standard. The calculation showed that the train-track-overhead system works well and meets the design requirements of the overhead system when the train passes through the reinforced line at a speed not exceeding 60 km/h.  
(2) The vibration response of the two types of overhead systems increases with speed, and the wheel rail lateral force is the most sensitive, when taking into account the impact of vehicle speed on the entire system at the AARS irregularity level. Tracking the train's reaction, the risk of the vehicle body overturning increased when the vehicle speed hit 60 km/h, as the lateral acceleration of the vehicle body had exceeded the limit. When the vehicle was traveling at 80 km/h, the wheel rail lateral force was more than the permissible limit of 48 kN, which was readily capable of resulting in wheel rail peeling. The II overhead system had exceptional overall performance; however, the I overhead system's vertical acceleration in the middle of the span surpassed the specification's maximum vertical acceleration limit of 0.35 g when the vehicle was traveling at 100 km/h. In general, the vehicle bridge system functioned well and satisfied the design specifications of the overhead system when the vehicle speed was less than 60 km/h.  
(3) The damping factor of the bridge had a significant influence on the transverse and vertical acceleration of the transverse and vertical spans but had little influence on their transverse and vertical displacement. It can be concluded that increasing the bridge damping ratio can improve the structure's seismic performance.  
(4) It is challenging to fully take into account the actual wheel-rail contact's complexity as well as the numerous factors that have an impact on the train track bridge coupling system. The resonance of the train bridge caused by train load requires further discussion because only one train model was taken into consideration in this paper, and neither the no-load nor heavy-load grouping of the train was taken into account.  
Figure 21: The impact coefficient varies with the damping ratio of trains crossing the bridge.  
**Author Contributions:** All authors substantially contributed to this work. [PERSON] performed the theory analysis. [PERSON] and [PERSON] established the FEM model. [PERSON] and [PERSON] wrote the paper. [PERSON] revised and finalized the paper. All authors helped with the writing of the paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was financially funded by the Natural Science Basic Research Program of Shaanxi (2022)Z-32), and the Fundamental Research Funds for the Central universities (300102212212).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.