# Dynamic Analysis of CRTS II Ballastless Track-Vehicle System Based on Moving Unit Method
## 6 Conclusions  
In this study, a new vibration analysis calculation model of the CRTS II ballastless track-vehicle coupled system was established using the moving unit method, and a calculation program was prepared. The model's dynamic response at different traveling speeds with or without consideration of the track slab discontinuities and track unevenness was investigated, and the following are the main conclusions:  
1. In the simple harmonic shape of the track uneven conditions, the dynamic response of each structure with the increase in the velocity of travel increased, which is the most significant steel rail dynamic response, while the concrete foundation and dynamic response of the rail slab, compared to the steel rail, decreased step by step. This is \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Rail Power Response**} & \multicolumn{5}{c}{**Percentile (\%)**} \\ \cline{2-6}  & **2–30** & **2.5–30** & **3–30** & **3.5–30** & **4–30** \\ \hline Displacement amplitude (mm) & 1.581 & 1.432 & 1.377 & 1.350 & 1.338 \\ Wheel-rail contact force Amplitude (kN) & 121.050 & 110.601 & 104.347 & 97.472 & 92.955 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Steel rails dynamic response under different wavelength range excitations. Figure 12: Comparison of steel rails dynamic response under different wavelength range excitation: (**a**) comparison of steel rails vertical displacement time curves; (**b**) comparison of wheel-rail contact force-time curves. due to the fact that the vibration has a high-frequency characteristic, and the dynamic response of the rails decreased layer by layer through the damping effect of the rail mat and CA mortar. 2. The comparison of the system's dynamic response under the two cases of considering and not considering the discontinuity of the rail slab showed that the dynamic response of each structure, except the acceleration of the vehicle, was greater than that of the continuous case of the rail slab, and the discontinuity of the steel rail's slab had less influence on the vertical acceleration of the vehicle and did not affect the smoothness of the traffic. 3. Under the influence of the random process unevenness of the time domain sample generated by using the Chinese rail spectrum, the time course of the rail dynamic response showed a strong random characteristic. Changing the unevenness parameter, it was found that, as the unevenness amplitude increased, the amplitude of the dynamic response fluctuation of steel tracks increased and the vibration became more intense; as the unevenness wavelength decreased, the steel tracks dynamic response increased significantly, the maximum in the wavelength range of 2-30 m; and as the unevenness sample wavelength increased, the oscillation degree of the dynamic response time course curve decreased significantly and tended to be smooth. The most important feature of the random process irregularity is that the shorter wavelengths showed instantaneous high-frequency pulse peaks, which caused the wheel-track impact in a short amount of time and made the wheel-track contact force increase sharply. Due to the complexity of the vehicle-ballastless track coupling system, the research work described in this paper did not examine the system thoroughly enough; thus, it is still necessary to continue to study the failure damage and temperature deformation in the field of ballastless tracks in the future, and to study a better ballastless track model to direct the construction and maintenance of high-speed railways. Conceptualization, T.L. ; Methodology, J.X. and L.X. ; Software, T.J. and G.W. ; data curation, G.W. and L.X. ; Validation, L.X. and T.J.; Writing--original draft, T.L. and J.X. ; Writing--review and editing, T.L. ; Supervision, T.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the Natural Science Foundation of Shaanxi Province (Grant No. 2021 JM-178). Not applicable. Data availability Statement: Data are presented in the article.