## 3 Results and Discussion
### Bearer Displacement at Rail Seats  
From Figures 4-9, maximum bearer displacements at rail seat location, associated with different vehicle velocities and three cases, are depicted for six different positions. As observed from Figures 4-9, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mode No**} & \multicolumn{2}{c}{**FFU Bearer**} & \multicolumn{2}{c}{**FFU Bearer**} \\ \cline{2-4}  & **Experimental [20]** & **Numerical** & **Numerical** \\ \hline
1 & 68 & 69 & 25 \\ \hline
2 & 143 & 137 & 87 \\ \hline
3 & 247 & 214 & 150 \\ \hline
4 & N/A & 446 & 208 \\ \hline
5 & N/A & 832 & 296 \\ \hline
6 & N/A & 1030 & 445 \\ \hline
7 & N/A & 1322 & 641 \\ \hline
8 & N/A & 1850 & 870 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Natural frequencies of the bearer used in the model. Figure 3: Fast Fourier Transform of acceleration at rail seat position under the crossing nose. a distinctive difference results from the number of unsupported bearers for all cases. Expansion of unsupported track section can cause higher track deflection [4; 8]. The magnitude of deflection is strongly related to unsupported bearer position due to varying track stiffness along the turnout. Highest deflections are observed when the shortest bearers, which are laid after longest bearer to adjust transition between normal track section and S&C, are unsupported. The relative increase of displacements in those cases could reach up to 86%, 224% and 467% for one, two and three unsupported bearers, respectively. On the other hand, the lowest deflections are mostly observed when the bearers at the closure panel are unsupported. Track stiffness is relatively higher along this zone due to larger surface contact area supported by ballast bed. This can also cause higher bending moments attributable to higher track stiffness [12]. The maximum bearer displacements for one, two and three unsupported bearers at closure panel have 53%, 115% and 198% relative increase. In Figure 4, maximum displacement of unsupported bearers at normal track section is presented. The effect of vehicle velocity seems to have a limited impact on the maximum bearer displacement in different velocities, where one and two unsupported bearers are of interest. Nevertheless, it is perceptible that higher velocities cause higher bearer displacements on the occasion of three unsupported bearers. The maximum displacement of the middle bearer of three unsupported bearers increase 20%, when velocity goes from 10 m/s to 50 m/s. Similar findings are mentioned in [4] which demonstrates that three unsupported sleepers cause significantly higher sleeper displacements with parallel to vehicle velocities rather than one and two unsupported sleepers. It should be noted that one and two unsupported cases in [4] also suffer from slightly higher displacements with increased velocities, contrary to current study where track surface irregularities affecting significantly track-train interactions produce significant fluctuations in terms of sleeper displacement. Figure 4: The maximum displacement of bearers at rail seats when an unsupported bearer exists at normal track section. Figure 5: The maximum displacement of bearers at rail seats when an unsupported bearer exists under switch blade. Figure 6: The maximum displacement of bearers at rail seats when an unsupported bearer exists at closure panel. Figure 8: The maximum displacement of bearers at rail seats when the longest bearer is unsupported. Figure 7: The maximum displacement of bearers at rail seats when an unsupported bearer exists under crossing nose. The trend in normal bearers disappears for the unsupported switch panel bearers in Figure 5, despite having same bearer length with normal track section. Highest deflection is observed as 9 mm at 40 m/s for three unsupported bearer case. It is evident that switch blades can contribute significantly to track stiffness.