A New Method to Deduce the Mapping Relationship between A Track and A Long-Span Cable-Stayed Bridge Under Different Excitations

Urban rail transit is rapidly evolving, with long-span cable-stayed bridges becoming increasingly popular among engineers because of their adaptability. However, as the operation time of bridges with tracks increases, the combined effects of repeated wheel loads and various bridge system excitations, including temperature changes and shrinkage–creep, gradually alter the alignment of the main beam. Similarly, the track structure on the bridge deck also undergoes vertical displacement, leading to corresponding degradation in rail alignment. This study applies singular function theory and verifies its effectiveness in bridge mechanical analysis. For the steel spring floating plate track cable-stayed bridge system, the mapping relationship between the deformation of the bridge’s main beam and the track’s deformation under bridge system excitation is derived, integrating singular function theory with the theory of train–track–bridge dynamic interaction. By analyzing the force transfer mechanism of the track–bridge system under system excitation, this research examines the effects of different excitations on the coupled dynamic response of the train–track–bridge. These findings suggest that system excitations increase the dynamic response of the train–track–bridge system, which is crucial for improving the durability and reliability of urban rail transit infrastructure.