Beams on elastic foundations – A review of railway applications and solutions

Beam on elastic foundation theory is widely employed when studying railway track behaviour, for applications such as track dynamics, and noise and vibration. At a basic level, the use of a single continuous beam resting on a springs-in-series support is straightforward to implement and computationally efficient. However, it can also be extended to simulate the multi-layered and periodic nature of railway tracks, which typically comprise a variety of components. Further, these track models can also be coupled with both vehicle and subgrade models. Therefore, this paper presents a state-of-the-art technical review of beam on elastic foundation theory, including the exploration of recent advancements in the field. Firstly, a variety of modelling strategies and solution methods employed for the computation of track behaviour are reviewed. These include periodic and semi-periodic modelling approaches. Considerations for extending beam on elastic foundation approaches to include train-track interaction and track-ground interaction are then provided. Finally, using the aforementioned theory, benchmark solutions for three common problem types are given: railway noise, railway track dynamics and railway ground-borne vibration.