Calculation of vertical vibrations of the rail taking into account the anisotropy of the elastic modulus of the sub-rail base

Abstract

The paper presents a solution to the problem based on nonlinear differential equations describing the oscillation of the rail, taking into account the change in the anisotropy of the elastic modulus of the sub-rail base when moving a constant force along it, while the speed of movement is translational; the value of the maximum deflection of the rail (beam) is also found. When solving this problem, it is assumed that the rail is a beam lying on the elastic anisotropic base. The value of the elastic modulus, which depends on the deflection value, is also taken into account; also, taking into account the linear correction along the ou axis, a second-order correction along the ox axis is taken into account, while the deflection size corresponding to the maximum value is determined. The obtained analytical expressions and numerical analysis, taking into account the anisotropy of the elastic modulus of the sub-rail base, allows us to predict and consider the amount of deflection under the influence of a constant force P, reducing the resistivity and energy consumption. The general methodology and mathematical procedures for predicting and optimizing the maximum deflection value are described, considering various factors of variable stiffness of the sub-rail base, taking into account the linear correction, which makes it possible to establish the basic laws of the dependence of operational characteristics on the anisotropy of the base on the deflection value corresponding to the maximum value.