## 5 Conclusions  
To investigate the vibration performance of the composite sleeper-ballasted track, the vehicle-track dynamic coupling model was established with consideration of the viscoelastic properties of the composite sleeper. Compared with the traditional type-III pre-stressed concrete sleeper, the power flow method was used to reveal the vertical distribution and the power flow transfer characteristics of the composite sleeper-ballasted track. The main conclusions are as follows:  
(1) From the perspective of the power flow of the track structure, the viscoelastic properties of the composite sleeper have a small effect on the rail power flow and have a greater impact on the power flow of the sleeper and the ballast bed in some frequency ranges. In the analysis, the viscoelastic properties of the composite sleeper should be considered, which can effectively improve the calculation accuracy of the power flow of the track structure;  
(2) Due to its own physical characteristics, the energy consumed by the vibration process of the composite sleeper is larger than that of the type-III pre-stressed concrete sleeper, which reduces the power flow of the ballast bed, especially in the ranges of 80-125 Hz and 250-400 Hz. This is beneficial to slowing down the pulverization of the ballast bed;  
(3) The power flow of the composite sleeper varies greatly along the longitudinal distribution; however, the power flow of the concrete sleeper is more evenly distributed along the longitudinal direction. The excessive vibration energy from the composite sleeper's rail-seat section may cause fatigue damage under long-term vehicle loading, requiring increased attention;  
(4) The temperature change mainly affects the power flow of the composite sleeper track structure in the frequency range above 50 Hz and has little effect on the rail or ballast bed. Relatively speaking, it has a slightly greater impact on the sleeper power flow. The higher the temperature, the smaller the modulus of the composite sleeper and the better the vibration reduction effect of the track bed;  
In this paper, the power flow method was used to investigate the vibration characteristics of composite sleeper-ballasted tracks in high-speed railways. In the future, the vibration characteristics of a composite sleeper-ballasted track in a heavy haul railway or subway could be investigated to provide theoretical guidance for the further use of composite sleepers in China.  
Conceptualization, Z.Z., Y.G. and C.L.; methodology, Z.Z. and C.L.; software, Z.Z. and Y.G.; validation, Z.Z., Y.G. and C.L.; formal analysis, Z.Z.; investigation, Z.Z. and C.L.; data curation, Z.Z.; writing--original draft preparation, Z.Z.; writing--review and editing, Y.G. and C.L.; visualization, Z.Z.; supervision, C.L.; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 51778543, and Chengdu-Lanzhou Railway Special Project, grant number CLRQT-2016-006. The authors express gratitude to [PERSON] and [PERSON] for their valuable suggestions. The authors declare no conflict of interest.