Railway track structural dynamics via periodic approaches

Periodicity can be defined as the repetitive character of a structure's features. In railway track systems, periodicity can be found in the geometrical and material properties in the train passage direction. For example, the repeating pattern of sleepers, rail seats or slab track units. To take advantage of this, this paper employs the direct periodic method, a novel numerical method which exploits the invariant nature of the railway track structure. Instead of simulating the total track domain, the direct periodic method studies a discrete portion of the track, often known as the reference cell, which captures its repetitive pattern and provides the total track response. First, the cell response is obtained by enforcing compatibility conditions within its system of equations of motion in the wavenumber-frequency domain. Then, the total space response is retrieved by replicating the cell's solution via a combination of periodic conditions and Fourier transformations. It is combined with perfectly matched layers to simulate infinite depth soil boundary conditions. Thus, this paper employs the direct periodic method in combination with perfectly matching layers to analyze track-ground dynamic interaction.