Predicting the dynamic response of slab track with continuous slabs under moving load TRAIAN MAZILU Department of Railway Vehicles, University Politehnica of Bucharest, Splaiul Independentei, 313, Bucharest 060032, Romania trmazilu@yahoo.com Abstract: - The paper discusses the problems of modeling and simulation of the dynamic response of slab track with continuous slabs under moving loads. The equations of motion are solved following three steps. First, the equations are transformed from the time-domain to the frequency-domain via the Fourier transformation method. Second, the solution of the transformed equations is obtained using the properties of the Green’s function of the differential operator associated to the aforementioned equations. Finally, the solution in the time-space domain results from the inverse Fourier transform. The response of the slab track to the stationary harmonic load is analyzed. The displacement pattern of the rail for various frequencies and velocities of the load is presented. Key-Words: - slab track, rail, bending wave, Doppler effect 1 Introduction This paper is dedicated to the analysis of the dynamic response of slab track with continuous slabs due to the moving harmonic load, which moves uniformly along the track. As it is known, the slab track is applied for high-speed lines [1] and for urban railway environment [2] - and this kind of problem represents the starting point for the studies related by the wheel/rail interaction. Usually, the structure of the slab track is composed of a massive concrete slab, into which the rails are embedded by means of Corkelast. Assuming that the two rails are symmetrically loaded, only half-track is required for modelling. Consequently, the slab track model is reduced to an infinite homogenous structure consisting of two beams continuously supported by elastic layers. The upper beam describes a rail, the lower one models the slab, while the two elastic layers reflect the properties of the rail pad and the track subsoil. Similar models were used to study the slab track response to a moving load [3, 4] or the interaction between a moving vehicle and the slab track [5, 6]. In order to solve the issue of the slab track response to moving load, many methods have been proposed. The direct method treats the input force as a boundary condition for the problem. More precisely, the input force is described for the right semi-infinite structure as a boundary condition on its left end. For the left semi-infinite structure, the input force is described as a boundary condition on its right end. For the case of non-moving load, the entire structure has the property to be symmetric. Due to symmetry, it is enough to analyse only the right semi-infinite structure. The Fourier transformation method treats the load as a part of the differential equation. The governing differential equations of the slab track are transformed to the wave number-frequency domain. Then, the transformed equations are simplified and transformed back to the space-time domain using the results of contour integration from the theory of complex variables or the inverse discrete Fourier transform (numerical method). The method of coupling in the wave number- frequency domain splits the model of the slab track into two structures, the rail and the slab on elastic foundation. These two structures are coupled via rail pad, which is uniformly distributed longitudinally. Applying this method, the frequency response functions of the two structures has to be separately found in the wave number-frequency domain. In this paper, a different method is proposed. Starting from the governing differential equations, the Fourier transform is performed to obtain the transformed equations in the frequency-domain. Then, the transformed equations are solved using the Green’s function of the differential operator belonging to the transformed equations. Finally, the inverse Fourier transform is utilized to find the solution of the problem. This method is analytical one and seems to be simpler. Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering ISSN: 1790-2769 22 ISBN: 978-960-474-080-2