MODELING OF RAILWAY TRACK OPERATION AS A SYSTEM OF QUASI-ELASTIC ORTHOTROPIC LAYERS

In this paper the authors give a solution to the problem of the impact of a rolling stock on the rail track on the basis of modeling a railway track as a multi-layered space, introducing each of the layers is a quasi-elastic orthotropic layer with cylindrical anisotropy in the polar coordinate system. The article describes wave equations, taking into account the rotational inertia of cross sectional and transverse shear strains. From the point of view of classical structural mechanics train path can be represented as a multilayer system comprising separate layers with different stiffness, lying on the foundation being the elastic-isotropic space. Winkler model provides that the basis is linearly deformable space, there are loads influencing its surface. These loads are transferred through a layered deformable half-space. This representation is used in this study as an initial approximation. For more accurate results of the deformation of a railway track because of rolling dynamic loads it is proposed to present a railway track in the form of a layered structure, where each element (assembled rails and sleepers, ballast section, the soil in the embankment, basement soils) is modeled as a planar quasi-elastic orthotropic layer with cylindrical anisotropy. The equations describing the dynamic behaviour of flat element in a polar coordinate system are hyperbolic in nature and take into account the rotational inertia of the cross sectional and the transverse shear strains. This allows identifying the impact on the final characteristics of the blade wave effects, and oscillatory processes. In order to determine the unknown functions included in the constitutive equations it is proposed to use decomposition in power series in spatial coordinate and time. In order to determine the coefficients of ray series for the required functions, it is necessary to differentiate the defining wave equations k times on time, to take their difference on the different sides of the wave surface, and apply the consistency condition for the transition from the jump of the derivative of a function in the coordinate to the jump of the derivative of a sought function in time of higher order. The proposed approach allows considering the whole structure of the railway track in the form of a set of layers, making for each layer (rail - sleeper; sleeper - ballast; ballast - ballast bed) a system of equations and solving them. Therefore it is possible to vary the characteristics of different layers and their modules of elasticity, determining the optimal thickness of the ballast layer or oversleeper and undersleeper strips