Mathematical Modeling of the Interaction of a Metal Bridge Superstructure with Rolling Stock

This study presents a comprehensive numerical analysis of the interaction between a metal bridge superstructure and rolling stock, focusing on the dynamic stability of empty freight gondola cars with worn wheel profiles. Using finite element modeling and validated experimental data, the research identifies critical speed thresholds at which transverse oscillations of the superstructure become hazardous. Results indicate that for speeds up to 80 km/h, safe operation is maintained under normal conditions. However, at 90 km/h, resonance occurs due to the alignment of the bridge’s natural horizontal bending frequency with the frequency of transverse wheel-rail impacts caused by bogie wobbling, leading to oscillation amplitudes of 11 mm, which exceed permissible limits. Furthermore, the study establishes that the elastic and inertial properties of the 55 m-span bridge structure influence rolling stock stability by approximately 15%. It is recommended that speed restrictions be imposed on freight wagons equipped with non-modernized 18-100 bogies, limiting their operation to a maximum of 90 km/h on both track beds and bridge spans to prevent derailment risks. The findings highlight the necessity for continuous track monitoring, bogie design improvements, and potential damping solutions for bridge structures to enhance railway safety. Future studies should incorporate wind and seismic effects to further refine operational guidelines. These results provide essential insights for railway engineers and infrastructure planners, contributing to the optimization of rolling stock movement and bridge design for modern freight transportation systems.