## 4 Results and Discussion
### Buffer Measure
#### 4.3.3 Effectiveness of the Buffer Structure  
A dynamic model of the three-carriage CRH3 train was established in UNIVERSAL MECHANISM (UM). Each carriage consists of, from top to bottom, the car body, the secondary suspension, the frame, the primary suspension, the axle box, and the wheelset. The car body, bogie frame, axle box, and wheelset are assumed to be rigid, with no deformation of vehicle components. The car body, bogie, and wheelset are all considered to have 6 degrees of freedom, while the axle box is considered to have only 1 degree of freedom (pitch), totaling 50 degrees of freedom. Both the primary and secondary suspensions are modeled using spring-damping elements, with viscous elastic linear force-element simulations employed in UM. Additionally, with the CRTSII-type slab ballastless track and box girder as the research subjects, the finite element software ABAQUS is employed to construct a three-dimensional geometric model of the track-bridge system. Modal analysis and mass structure analysis are conducted to generate a flexible file that can be utilized by UM, which is subsequently imported into UM for further processing. The track-bridge model comprises the following components, listed from top to bottom: rail, fasteners, rail support groove, track slab, mortar layer, base slab, and flat box girder. The rails are modeled using CHN60 rail with Timoshenko beam elements. The fasteners are represented by three-dimensional spring-damper elements, while the track slab, mortar layer, and base slab are modeled using solid elements. The bridge is also represented with solid elements, taking into account the impact of the bridge shape on the aerodynamic loads from the train. Binding constraints are applied between the track slab and both wide and narrow cracks, between the track slab and the mortar layer, between the mortar layer and the base slab, and between the base slab and the bridge deck. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Aerodynamic Load**} & \multirow{2}{*}{**Carriage**} & \multicolumn{2}{c}{**Without**} & \multicolumn{2}{c}{\(D\)} \\  & & **Buffer Structure** & & \\
**Coefficient** & & \(\Delta C\) & **45 m** & **90 m** & **135 m** \\ \hline \multirow{3}{*}{\(C_{D}\)} & Head & 0.0944 & 6.93\% & 10.04\% & 10.83\% \\  & Middle & 0.0339 & 5.38\% & 8.01\% & 8.53\% \\  & Tail & 0.0273 & 18.08\% & 28.13\% & 29.04\% \\ \hline \multirow{3}{*}{\(C_{L}\)} & Head & 0.0763 & 5.51\% & 7.92\% & 8.34\% \\  & Middle & 0.0563 & 1.71\% & 5.70\% & 6.17\% \\  & Tail & 0.0272 & 8.39\% & 10.85\% & 11.07\% \\ \hline \multirow{3}{*}{\(C_{M}\)} & Head & 0.0134 & 10.68\% & 15.68\% & 16.13\% \\  & Middle & 0.0040 & 2.53\% & 5.81\% & 6.42\% \\ \cline{1-1}  & Tail & 0.0089 & 1.24\% & 2.70\% & 3.17\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Decrease rate in the amplitude of changes in aerodynamic load coefficients of HST when installing a buffer structure of different lengths. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Aerodynamic Load**} & \multirow{2}{*}{**Carriage**} & \multicolumn{2}{c}{**Without**} & \multicolumn{2}{c}{\(D^{\prime}\)} \\  & & **Buffer Structure** & & \\
**Coefficient** & & \(\Delta C^{\prime}_{\text{max}}\) & **45 m** & **90 m** & **135 m** \\ \hline \multirow{3}{*}{\(C_{D}\)} & Head & 0.6177 & 31.41\% & 55.59\% & 56.97\% \\  & Middle & 0.1394 & 40.77\% & 59.66\% & 60.94\% \\  & Tail & 0.1506 & 38.15\% & 54.18\% & 57.10\% \\ \hline \multirow{3}{*}{\(C_{L}\)} & Head & 0.3386 & 39.14\% & 54.63\% & 55.56\% \\  & Middle & 0.1629 & 52.48\% & 66.30\% & 66.13\% \\  & Tail & 0.1094 & 8.27\% & 18.11\% & 15.88\% \\ \hline \multirow{3}{*}{\(C_{M}\)} & Head & 0.0943 & 30.82\% & 49.55\% & 50.76\% \\  & Middle & 0.0151 & 21.07\% & 29.44\% & 31.48\% \\ \cline{1-1}  & Tail & 0.0301 & 42.19\% & 57.81\% & 59.42\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Decrease rate in the amplitude of the rate of changes in aerodynamic load coefficients of HST when installing a buffer structure of different lengths.