# Vibration Response Analysis of Overhead System Regarding Train-Track-Bridge Dynamic Interaction
## 3 Coupling Vibration Analysis of Train-Track-Overhead System
### Influence of Train Speed on the Dynamic Response of Train Bridge System  
AAR5 was chosen to examine the impact of train speed on the dynamic response of the train bridge system to track irregularity. A 20 km/h increment was used to increase the train's speed from 20 km/h to 100 km/h. Since the train's loading must be stable for some time, the train is programmed to begin loading at 20 m from the overhead system. The system's dynamic indexes are shown in Tables 10 and 11, with the nonconformity index represented by \({}^{\star\star\star}\). According to the above table, all of the indexes of the two types of structures generally increase with speed, with the transverse force of wheel and rail being the most sensitive to speed change, owing to the large loading force on the overhead system at high train speeds. Additionally, according to the train's response, the lateral acceleration of the train body has exceeded the limit when the speed reaches 60 km/h, which could result in the train body overturning. When the speed reaches 80 km/h, the lateral force of the wheel and rail is greater than the permissible limit of 48 kN, which is easily capable of resulting in wheel-rail stripping. The II overhead system performs superbly, according to observations of the two different types of overhead systems. At a speed of 100 km/h, the I aerial system's span experiences a vertical acceleration greater than 0.35 m/s\({}^{2}\), in accordance with the standards for vertical acceleration, specifically the maximum vertical acceleration threshold. In general, the train bridge system functions well and satisfies the design specifications of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Overhead** & **Speed** & **Dezilment** & **Lateral** & **Acceleration** & **Lateral** & **Wheel Weight** & **Superling Index** \\
**System** & **(km/h)** & **Coefficient** & **Force (kh)** & **(m/s\({}^{2}\))** & **Acceleration** & **Reduction Rate** & **Vertical** & **Lateral** \\ \hline \multirow{6}{*}{I} & 20 & 0.71 & 21.45 & 0.17 & 0.27 & 0.53 & 0.97 & 0.57 \\  & 40 & 0.64 & 33.08 & 0.30 & 0.88 & 0.54 & 0.98 & 1.93 \\  & 60 & 0.69 & 41.69 & 0.29 & *1.04* & 0.60 & 1.65 & 2.82 \\  & 80 & 0.73 & *48.55* & 0.29 & *1.38* & 0.73 & 1.31 & 2.42 \\  & 100 & 0.81 & *56.06* & 0.31 & *1.98* & *1.07* & 1.73 & 2.89 \\ \hline \multirow{6}{*}{II} & 20 & 0.49 & 18.90 & 0.09 & 0.19 & 0.38 & 0.78 & 1.32 \\  & 40 & 0.50 & 23.20 & 0.39 & 0.74 & 0.43 & 1.18 & 1.77 \\ \cline{1-1}  & 60 & 0.51 & 30.96 & 0.25 & *1.17* & 0.67 & 0.92 & 1.62 \\ \cline{1-1}  & 80 & 0.61 & 38.02 & 0.31 & *1.26* & 0.75 & 1.54 & 2.31 \\ \cline{1-1}  & 100 & 0.83 & 45.10 & 0.34 & *1.40* & 0.95 & 1.71 & 2.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Response of trains crossing the bridge at different speeds. (\({}^{\star\star\star}\) is displayed for any data that do not meet the specifications). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Overhead** & **Speed** & **Vertical** & **Lateral** & **Vertical** & **Lateral** \\
**System** & **(km/h)** & **Deflection** & **Displacement** & **Acceleration** & **Acceleration** \\  & & **(mm)** & **(mm)** & **(mm/s\({}^{2}\))** & **(m/s\({}^{2}\))** \\ \hline \multirow{6}{*}{I} & 20 & 2.06 & 0.13 & 0.62 & 0.06 \\  & 40 & 2.15 & 0.14 & 1.75 & 0.10 \\ \cline{1-1}  & 60 & 2.20 & 0.19 & 2.71 & 0.15 \\ \cline{1-1}  & 80 & 2.35 & 0.20 & 3.20 & 0.27 \\ \cline{1-1}  & 100 & 2.62 & 0.16 & *3.88* & 0.41 \\ \hline \multirow{6}{*}{II} & 20 & 2.83 & 0.19 & 0.27 & 0.13 \\ \cline{1-1}  & 40 & 2.84 & 0.21 & 0.79 & 0.08 \\ \cline{1-1}  & 60 & 2.79 & 0.21 & 1.04 & 0.12 \\ \cline{1-1}  & 80 & 2.87 & 0.24 & 1.41 & 0.17 \\ \cline{1-1}  & 100 & 2.93 & 0.26 & 1.82 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The response of the overhead system at different speeds. the overhead system when the train speed is less than 60 km/h. Then, I overhead system data is chosen, various index changes with speed curves are examined, and a thorough analysis of the outcomes is carried out under various intuitive reaction conditions.