Simplified Analytical Approach to Vertical Response of High-Speed Train-Bridge Systems on Track Irregularities

Abstract

This study proposes a simplified analytical approach for evaluating the vertical dynamic response of a high-speed train–track-bridge system subjected to rail irregularity excitation. In the theoretical model, the car body and bogie frame of the train, together with the rail, sleeper, and ballast of the track, are represented using a lumped-parameter method, with their degrees of freedom interconnected through spring–damper elements. The bridge is separately idealized as a simply supported Euler-Bernoulli beam. This modelling strategy enables the dynamic interaction between the moving train and the track system to be considered while maintaining a relatively simple computational framework. The dynamic interaction between the train and the track under sinusoidal rail irregularities is simulated in MATLAB/Simulink to obtain time-varying axle loads. These dynamic axle loads are subsequently applied to the bridge to compute the vertical midspan displacements using the energy-based moment–area method. In the numerical analysis, three rail irregularity profiles are considered, characterized by representative amplitude-wavelength pairs of (1.5 mm, 3.0 m), (3.0 mm, 12.5 m), and (6.0 mm, 50.0 m). The train parameters correspond to the Thalys central carriage, while the bridge adopted in the simulations is a 24 m simply supported box girder. Train speeds of 200, 250, and 300 km/h are investigated to examine the effects of operating speed and rail irregularity characteristics on the dynamic response of the coupled system. The results indicate that the dynamic axle loads and the corresponding bridge displacements are approximately 1.65 to 1.93 times greater than those induced by equivalent static loads. These findings demonstrate the strong influence of train speed and rail irregularity intensity on bridge vibrations and highlight the importance of considering dynamic interaction effects in the evaluation of high-speed railway structures. Overall, the proposed approach provides a practical and efficient tool for evaluating the dynamic performance and safety of railway bridges subjected to high-speed train operations, while avoiding the computational complexity associated with more sophisticated numerical models.