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The article deals with such important concept as the resonance to three cases: when rolling stock is described by a system of linear differential equations with constant coefficients, when the mathematical model of rolling stock represented a nonlinear system of differential equations, and when in the latter we take into account the multiplicative disturbance from railway, namely its non-equal-elasticity between sleepers. In this case, speak properly and correctly is not about a particular value of RMS-velocity, but on parametric instability areas.

The article is devoted to the accounting problem of longitudinal non-equal-elasticity of railway track which led to forced vibrations for non-spring mass of rolling stock are interacting with multiplicative perturbation, that is increasing the amplitude of the bouncing wheel pair, or reducing it. This depends on the phase relationship between these influences .

The article devoted to results of the longitudinal multiplicative perturbation effect from railway track in relation to rolling stock.There is the technique for finding of difference type Raman resonances areas,which based on the theory of division in slow and fast components for motion of dynamic system.It proves a fact that the RMS-velocity for motion of the train is not a specific numerical value,but that is an area for which the width depends on the multiplicative factor driving

Based on the proposal for the formation of a railway track for operational deployment without ballast using a sub-rail base with a viscoelastic element forcedly filled with Newton's fluid and laid on an unprepared surface without ballast, an example of calculating the interaction of a wheel and a rail with this element based on the energy method is given. The possibility of using the design of the under-rail device for the operational laying of a railway track in difficult conditions on an unprepared surface without a track ballast layer is substantiated. The elastic dynamic impact of a wheel on a rail with initial speeds along a sub-rail base in the form of a box with shells laid on an unprepared surface is considered. The kinetic energy of a wheel hitting a rail laid on the proposed under-rail base passes not only into the potential energy of deformation, but also into the energy of wave and oscillatory processes. To improve the accuracy of solving the problem of dynamic impact, the transition of a part of the energy into the energy of local deformations in the contact area of the wheel with the rail is taken into account. Within a short period of time after touching the wheel at a certain speed, all elements of the rail acquire a certain strain rate. It is assumed that at the moment of contact with the wheel, the rail does not change its original shape, and the decrease in the speed of the wheel occurs due to local deformation of the materials of the contacting bodies; this period of impact will last until the velocities of the two bodies are equalized, after which the shape of the middle surface of the rail, modeled by a Bernoulli-Euler beam, will begin to change. Since the kinetic energy of the wheel is converted into the potential energy of bending, it is taken into account in the calculation to take into account the mass of the impacted body as the load of the wheel on the rail.