The Wavelength Characteristics of Vertical Deformation and a Train Dynamics Simulation of Long-Span, Cable-Stayed Bridges Under Complex Loads

Ballastless tracks have a high smoothness, but the corresponding laying requirements are strict. Therefore, the maximum span of cable-stayed bridges that can accommodate ballastless tracks is 392 m. For laying ballastless track structures over larger spans, the deformation characteristics of long-span, cable-stayed bridges under complex loads are incompletely understood, and the interaction between them and long-span track-bridge structures is unclear. The influence of the wavelength of the cosine wave on the track-bridge mapping of different orbital structures was explored. The wavelength characteristics of vertical deformation under complex loads were investigated. The track-bridge integrated model for the cable-stayed bridge was established to analyze the mapping relationship between the rail and the bridge and the wavelength characteristics of deformation. Based on the mapping relationships and the wavelength characteristics of deformation, the train-track-bridge dynamics simulation model was simplified. The results show that, when the minimum wavelength of bridge deformation surpassed 6 m, 10 m, and 16 m, the rail deformation in the ballasted track, the longitudinal-connected track, and the unit slab-type ballastless track accurately mirrored the deformation of the bridge. For the span of bridges ranging from 200 m to 600 m, the wavelength of vertical deformation ranged from 21 to 1270 m under complex loads. During local loads, the vertical deformation below the 200 m wavelength constituted a significant proportion near the pie. Considering the influence of the deformation on the train vibration response, the train-bridge dynamic coupling model can be employed to treat the track structure as a load to reduce the complexity of the model and enhance the calculation efficiency.