Keywords: two layer model, rail track dynamics, nonlinear response, semi-analytical method.

Seeking of new models, especially highly valued analytical ones which are useful for parametrical analysis of rail track dynamics, is still of importance. The simplest model is represented by a beam resting on elastic or viscoelastic foundation. This model is good enough for the analysis of rails but all parameters of rail foundation must be averaged and therefore it is impossible to study the behaviour of specific components of rail track structure. In the case of two layer model, in which the first layer represents rails and the second one sleepers, the solution becomes very complicated. Both mentioned models have been already solved and validated under assumption of nonlinear foundation stiffness. Nonlinear stiffness of rail fastening systems is a factor arising from experimental measurements. It can have significant influence on the rail track behaviour and this phenomenon is not checked so far. Therefore inclusion of additional nonlinearity in the two layer model based on double beam system is an interesting direction of further investigations being natural extension of previous works. In this paper, a model consisting of two infinitely long beams representing rails and sleepers, and connected by a viscoelastic nonlinear layer, rests on nonlinear foundation. The existence of two nonlinearities makes the system computationally difficult and the detailed analysis of its stability and solution convergence is needed before application to the real rail track investigation. The two layer model of rail track built on the basis of a double beam system has been solved under assumption of two nonlinearities describing foundation and fastening system stiffness. The proposed computational approach using a hybrid semi-analytical method, involving the wavelet analytical approximation combined with the Adomian’s decomposition, allows obtaining the solution in the physical domain for vertical vibrations of rails and sleepers. The model solution together with computational examples are presented along with methodological guidelines allowing its engineering application. The form of solution makes the parametrical analysis efficient, leading to reliable discussion of the investigated factors influence on the rail track system dynamic response to moving train. The obtained solution for the two layer model with two nonlinear factors is an important novelty giving possibility of the particular rail track components effects investigation.

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