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

Abstract

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.