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Phenomena associated with railway dynamics are usually analysed by using numerical approaches due to high computational complexity of such systems. However, classical methods based on analytical modelling are still highly valued and desirable by researchers and railway industry. This paper presents analytical solution representing dynamic response of railway due to moving train. Two nonlinear models are analysed. The first one assumes that the Euler-Bernoulli beam represents rail resting on viscoelastic foundation with nonlinear stiffness [1]. The second one consists of two layers: the upper one which is modelled by the Euler-Bernoulli beam on viscoelastic foundation, representing rail with fasteners, and the lower one which represents sleepers (rigid bodies without bending) [2]. This system rests on nonlinear viscoelastic foundation modelling ballast and subgrade. In both cases, the beam is subjected to a load moving with constant velocity and consisting of a set of forces produced by wheelset of train. Wheels produce excitations harmonically varying in time with frequency associated with the rail head wear. The solutions of the systems described by differential equations are obtained by applying the Fourier transform combined with Adomian’s decomposition and wavelet based approximation [1, 2]. It is shown that both models give good enough representation of railway dynamics in some range of parameters when one deals with rail displacements. These results are verified by comparison of the obtained solutions with measurements carried out for fast train Pendolino EMU250 on Polish rail network [3]. However, analysis of other characteristics, involving derivatives of higher orders, might lead to wrong results, especially in the case of rail bending stress calculation. Some examples of physical parameters giving stresses exceeding limit values are shown. This problem does not disappear when one deals with other analytical methods based on application of the Fourier transform. Possible reasons of this issue are pointed out and some ways of further investigations are proposed in order to improve the undertaken analysis.
References:
[1] P. Koziol, Experimental validation of wavelet based solution for dynamic response of railway track subjected to a moving train. Mechanical Systems and Signal Processing, 79, 174-181, 2016.
[2] P. Koziol, Wavelet approximation of Adomian's decomposition applied to the nonlinear problem of a double-beam response subject to a series of moving loads. Journal of Theoretical and Applied Mechanics, 52, 3, 687-697, 2014.
[3] W. Czyczula, T. Tatara et al., Field investigation of track response under EMU-250 (Pendolino) high speed train (in Polish). Cracow University of Technology reports. Krakow 2014.