# Dynamic Analysis of CRTS II Ballastless Track-Vehicle System Based on Moving Unit Method
## 5 Simulation Analysis of Random Process Orbital Unevenness
### Effect of Uneven Wavelengths on Dynamic Response  
As short-wave irregularities are the most damaging to the operation and maintenance of high-speed rail, the analysis was focused on a shorter wavelength track unevenness in the wavelength region of 30 m or less. The 63.2% percentile spectrum of the ballastless track of Chinese high-speed rail was taken as the external excitation, and the traveling speed was fixed at 350 km/h. Four sets of random track unevenness samples with different wavelength ranges were taken. After the simulation, the dynamic response of the steel rails under different wavelength ranges of the track unevenness excitation was obtained, and the extracted rail vertical displacement amplitude and wheel-rail contact force amplitude can be seen in Table 2. Figure 11a illustrates the comparison of steel rail's vertical displacement time range curves under a 2-30 m wavelength and a 4-30 m wavelength; Figure 11b illustrates the contrast of wheel-rail contact force-time range curves under a 2-30 m wavelength and a 4-30 m wavelength.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Rail Power Response**} & \multicolumn{3}{c}{**Percentile (\%)**} \\ \cline{2-4}  & **25** & **63.2** & **90** \\ \hline Displacement amplitude (mm) & 1.378 & 1.427 & 1.550 \\ Wheel-rail contact force & 95.264 & 108.647 & 129.546 \\ Amplitude (kN) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Rail dynamic response under different percentile spectrum excitation.  
Figure 11: Comparison of the dynamic response of rail under different percentile spectrum excitation: (a) comparison of rail vertical displacement time curves; (b) comparison of wheel-rail contact force-time curves.  
As can be seen from Table 2, under the condition that the amplitude of the track unevenness excitation is close, with such an increase in wavelength, the track displacement and wheel-rail contact force decrease significantly, and the magnitude of the decrease gradually slows down, among which the decrease between the displacement amplitude is 9.4%, 3.9%, 1.9%, and 0.8%, respectively, and the decrease between the wheel-rail contact force amplitude is 8.6%, 5.7%, 6.5%, and 4.6%, respectively; the change tends to be stable, and the variation is stable. As can be seen from the numerical trends in the table and the above analysis, shorter wavelengths of the unevenness of around 2 m have an important impact on the dynamic response of the wheel-rail and are more likely to lead to a deterioration in the track geometry and train operating safety.  
As illustrated in Figure 12, the steel rails' vertical displacement time curve oscillates up and down around the center of 1.2 mm, and the intensity of the curve oscillation increases as the wavelength of the track irregularity decreases; the wheel-rail contact force-time curve oscillates up and down around the center of 70 kN, and the intensity of the curve oscillation increases as the wavelength of the track irregularity decreases. As the wavelength increases, the dynamic response of the steel rails decreases significantly, and the curve tends to smooth out.