## 4 Influence Factors on Dynamic Responses of Vehicle-Track-Subgrade System in Transition Section
### Change Rule of Dynamic Response along the Longitudinal Direction of the Line
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Differential**} & \multicolumn{3}{c}{**Acceleration of Train**} & \multirow{3}{*}{\begin{tabular}{c} **Rate of Wheel** \\ **Load Reduction** \\ **Q/P** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Wheelset Vertical** \\ **Displacement** \\ **Q/P** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Rail Wheel Force** \\ **(kN)** \\ \end{tabular} } \\ \cline{3-8}  & & **Lateral** & & & **Q/P** & & **(mm)** & **Vertical** & **Lateral** \\ \hline
3 & 0.07 & 0.45 & 0.53 & 0.19 & 40.4 & 2.9 & 226.6 \\
4 & 0.12 & 0.67 & 0.79 & 0.25 & 57.7 & 3.7 & 238.0 \\
5 & 0.12 & 0.87 & 0.96 & 0.33 & 87.5 & 7.3 & 283.2 \\
6 & 0.19 & 3.49 & 2.88 & 1.46 & 139.2 & 9.4 & 294.2 \\
7 & 0.26 & 3.79 & 4.37 & 1.66 & 168.6 & 15.4 & 344.9 \\
7.4 & 0.50 & 4.93 & 8.48 & 2.21 & 183.3 & 56.1 & 558.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Influence of different differential settlements (mm) of road bridge transition sections on vehicle’s dynamic performance. The rigidity of the rail causes the irregularity of the rail surface, and the more serious the irregularity is, the larger the rail deflection difference is. The stiffness ratio of the transition section and common subgrade for the safety and stability of vehicle operation is not the main factor to control the dynamic characters of the transition section. On the other hand, the on-site investigation of the state of the road bridge transition section shows that as long as the track is frequently lifted and removed and the ballasted track is tamped for maintenance, the track surface is kept smooth, and the track inspection vehicle can pass smoothly without being deducted points. It can be seen from Figure 10 that with the increase in the transition angle \(\theta\), the amplitude of dynamic stress and displacement on the bed surface does not change significantly with the transition angle, but its amplitude changes differently in the longitudinal direction of the transition section. Table 1 shows that the vehicle lateral acceleration \(\mathbf{a}_{y}\), vertical acceleration \(\mathbf{a}_{z}\), wheel load reduction rate Q/P, Y/Y\({}_{\text{Derawment}}\), wheel pair vertical force, lateral wheel-rail force Q and so on increases in turn as the bending of the track surface increases. When the angle \(\theta=3/1000\), the acceleration of the vehicle has exceeded the design limit of 0.13 g; while when \(\theta=1/1000\), the acceleration of the vehicle is smaller than the design limit of 0.13 g. This confirms that the limit value of the angle of the ballastless track is 1/1000, which is reasonable. At the same time, the bending angle of the transition section has a more significant impact on the dynamic behavior of the vehicle body on the rail than the performance under the rail. As the dynamic performance changes such as vehicle acceleration and wheel load reduction rate are caused by track irregularity, after the length of transition section is determined, the dynamic performance of the vehicle body can be guaranteed as long as the bending angle is limited. Figure 10: Effect of angle change on dynamic response of subgrade surface layer: (**a**) dynamic stress; (**b**) dynamic displacement. Figure 9: Effect of stiffness change on dynamic response of subgrade surface layer: (**a**) dynamic stress; (**b**) dynamic displacement. It can be seen from Table 1 and Figure 11 that with the increase in differential settlement, the dynamic response of vehicle-track increases in turn. When the differential settlement h = 5 mm, most of the dynamic characteristics' evaluation indexes are less than the allowable values, and some indexes are close to the allowable values of the dynamic characteristics' control indexes, such as the wheel-rail load reduction rate, which reaches 0.96, and the vehicle body acceleration, which reaches 0.87 m/s\({}^{2}\). It can also be seen that the dynamic response of the transition section increases with the increase in differential settlement of the transition section.