Analysis of Train–Track–Bridge Coupling Vibration Characteristics for Heavy-Haul Railway Based on Virtual Work Principle

This paper introduces an innovative model for heavy-haul train–track–bridge interaction, utilizing a coupling matrix representation based on the virtual work principle. This model establishes the relationship between the wheel–rail contact surface and the bridge–rail interface concerning internal forces and geometric constraints. In this coupled system’s motion equation, the degrees of freedom (DOFs) of the wheelsets in a heavy-haul train lacking primary suspension are interdependent. Additionally, the vertical and nodding DOFs of the bogie frame are linked with the rail element. A practical application, a Yellow River Bridge with a heavy-haul railway line, is used to examine the accuracy of the proposed model with regard to discrepancy between the simulated and measured displacement ranging from 1% to 11%. A comprehensive parametric analysis is conducted, exploring the impacts of track irregularities of varying wavelengths, axle load lifting, and the degradation of bridge stiffness and damping on the dynamic responses of the coupled system. The results reveal that the bridge’s dynamic responses are particularly sensitive to track irregularities within the wavelength range of 1 to 20 m, especially those within 1 to 10 m. The vertical displacement of the bridge demonstrates a nearly linear increase with heavier axle loads of the heavy-haul trains and the reduction in bridge stiffness. However, there is no significant rise in vertical acceleration under these conditions.