Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartin [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de No and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given.