A Hybrid 3D Railway Track Model for High-Frequency Dynamics under Moving Loads

This paper presents a hybrid three-dimensional railway track model for high-frequency dynamics developed by combining the Wave Finite Element (WFE) method with standard Finite Element (FE) modelling techniques. The proposed approach enables the accurate representation of a wide range of railway track typologies, including both continuously supported configurations and tracks with discrete supports. Thanks to the WFE formulation, the model efficiently captures the high-frequency dynamic behaviour of the rail cross-section, which may play a crucial role in the generation of rolling noise in both tangent tracks and curved sections. The influence of moving load on the rails is also included in the hybrid FE–WFE model. This extends previous methodologies developed for simplified track models to a more advanced and realistic three-dimensional formulation, making it suitable for the analysis of high-frequency phenomena originating from the wheel-track interaction at high train speed. Three potential application scenarios are presented, including a conventional ballasted track, a booted sleeper track, and an embedded rail system with grooved rails. The results show that accounting for moving-load effects becomes important to accurately represent the complexity of high-frequency track vibrations at train speeds above 150 km/h, with a potential significant impact on rolling noise estimation for high-speed applications.