## 4 Results and Discussion
### Comparative Analysis of Composite Sleeper and Type-III Sleeper-Ballasted Track  
The advantages of composite sleepers include their excellent elasticity, which can increase the elasticity of the track structure and reduce the vibration of the substructure. In order to analyze the effect of the use of the composite sleeper track, its viscoelastic properties are considered and compared with the most widely used type-III concrete sleeper track in China. For convenience of comparison, the rail power flow values of the composite sleeper and type-III pre-stressed concrete sleeper-ballasted track at one-third octave frequency are shown in Figure 8. The rail power flow values are mainly concentrated below 100 Hz. At most center frequencies, the rail power flow values of the two tracks are relatively close. In a certain frequency range, the rail power flow changes slightly. At the center frequency of 63 Hz, the rail power flow of the composite sleeper-ballasted track is 4.2 dB less than that of the concrete sleeper-ballasted track. At the center frequency of 125 Hz, the former is 4.2 dB larger than the latter. From the perspective of the rail vibration energy, the use of the composite sleeper has little effect on the rail power flow. Figure 7: Power flow of track structure: (**a**) rail power flow; (**b**) sleeper input and output power flow; (**c**) ballast bed power flow. A comparison of the sleeper power flow values of the two ballasted tracks is shown in Figure 9. It can be observed that the composite sleeper input power flow is larger than that of the concrete sleeper at most of the center frequencies. This is due to the smaller mass of the composite sleeper when the wheel-rail forces are similar, resulting in a larger vibration velocity on the upper surface of the composite sleeper. At the center frequency of 800 Hz, the composite sleeper input power flow increases by 9.8 dB. The composite sleeper output power flow is close to or even smaller than that of the concrete sleeper at most of the center frequencies, which is caused by the elasticity and damping effects of the composite sleeper, while the power flow is more greatly consumed in the composite sleeper's internal transmission process. It can be clearly seen from Figure 9b that the internal vibration energy consumption for the composite sleeper is significantly larger than that of the concrete sleeper. At 315 Hz, the composite sleeper consumption power flow is 8.6 dB larger than that of the concrete sleeper. The above analysis can clarify the characteristics of energy transfer inside the composite sleeper. The vibration energy transmitted from the upper part to the composite sleeper is not reduced, and is even slightly larger than the concrete sleeper. The composite sleeper uses its own physical characteristics and the energy consumed by the vibration process is significantly larger than the concrete sleeper; compared with the concrete sleeper, in some frequency ranges, the energy transmitted downward from the composite sleepers is reduced. Figure 8: Rail power flow. Figure 9: _Cont._  
In order to investigate the power flow distribution of the sleeper under vehicle loading, the power flow of each node in the longitudinal sections of the bottom of the sleeper was calculated. In this way, the power flow of each section along the longitudinal direction of the sleeper can be obtained. Taking the longitudinal section of the sleeper, the frequencies, and the power flow as the x, y, and z coordinates, respectively, the power flow distribution along the longitudinal direction of the sleeper can be obtained, as shown in Figure 10.  
It can be observed from the figure that the vibration energy values of the sleeper are mainly concentrated in the range of 1-100 Hz, and that there are many peaks at different center frequencies, which are related to the track irregularity, track structure, and vehicle.