## 3 Results and Discussion
### Bearer Displacement at Rail Seats
In the figure, a perceptible decrease in the displacement value at 20 m/s is also believed to be a result of the dynamic response of the vehicle to track surface irregularities. This effect is obvious in the reference case as the higher velocities cause fluctuation on the result curve. In Figure 6, simulation outcomes for unsupported bearers at closure panel are given. Lowest maximum displacement values are mainly observed in this case. As aforementioned, track stiffness is relatively high at this section along the closure panel. The effect of different velocities is indistinct however, the number of unsupported bearer still have important effect. Among the deflection values, highest value is 5.87 mm for the case of three unsupported bearers with 50 m/s vehicle speed whereas the lowest displacement is 2.9 mm for one unsupported bearer at same speed. The corresponding value in the reference case is 2 mm of displacement. Similar behavior, occurs when the unsupported bearers emerge under the crossing panel (Figure 7) An interesting behavior could be realized in Figure 7. Although there is a trend of higher displacements with higher speeds, in general, three unsupported bearers do not fit that profile. For instance, the bearer displacements at 50 m/s compared to 10 m/s are higher for the reference, one and two unsupported cases. The differences are 0.3 mm, 0.4 mm and 0.7 mm, respectively. However, the displacement value for same condition is 0.1 mm less in the case of three unsupported bearer. It is apparent that three unsupported bearers enable a positive effect at 50 m/s. A similar behavior is found in [6] where the wheel-rail contact forces become stable subsequent to exceeding certain number of unsupported sleeper. The reason could be related to smooth transition between sleepers instead of sudden change. However, this positive effect could also be a result of limitation in the numerical model where the crossing nose is represented by beam elements. In Figure 8, the results of simulations for unsupported longest bearers and based on simulation case, unsupported shortest neighbor bearer are presented. In this case, the displacement values for longest bearers are higher when compared to bearers under crossing nose that are relatively in similar lengths. The section where the longest bearers are laid is close to physical separation point of two  
Figure 9: The maximum displacement of bearers at rail seats when the shortest bearer is unsupported. tracks. Therefore, the dependency between two tracks seems to be weak; and results in slightly lower track stiffness. In the case of one bearer, maximum displacements occur at unsupported bearers for all velocities. Displacement values are 3.1 mm, 3.8 mm, 4.1 mm, 3.7 mm and 3.2 mm from 10 m/s to 50 m/s, which indicates that a resonance like behavior could be observed and critical speed could be 30 m/s. For other cases, similar pattern is observed but up to speed of 40 m/s. It is noted that analysis interval of velocity parameter might be insufficient to show resonance effect. Another outcome that could be perceived from the figure is that in the case of three unsupported bearers, one of the unsupported bearer is the shortest bearer (bearer no. 62) that shows recognizable displacement similar to longest bearer no. 61). Interestingly, the other unsupported bearer (bearer no. 60), which has similar length with longest bearer, does not deflect in similar order with longest bearer, even though it shows similar deflection in the case of two unsupported bearers. It can be found that shortest Sleeper causes an asymmetrical loading. In Figure 9, deflections of unsupported shortest bearers are given. The effect of different velocity is obvious in three unsupported bearer case. Displacements of the bearer increase significantly from 10.3 mm to 13.1 mm with respect to velocity. A small decline at 20 m/s could be a result from any track surface irregularity or the sudden transition from the longest bearer to the shortest bearer.