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The subject of the research is a sub-rail foundation containing a viscous element. The purpose of the study is to evaluate the effect of including a viscous element in the elastic system (rails, sleepers, ballast, etc.) on the overall rigidity of a railway track. The design of a sub-rail foundation with a viscous element is described by the generalized Maxwell model and contains a shell filled with a Newtonian fluid, in particular air. Pneumatic shells with different thicknesses were considered. The modeling was carried out in the finite element analysis environment. Mathematical models of a track section with a sub-rail device containing a pneumatic shell were constructed. The calculation results showed the absence of a sharp increase in internal force factors and stress concentration in typical track sections when laying a sub-rail foundation with a pneumatic element. A change in the overall rigidity in the vertical plane did not lead to a significant change in bending stresses in the edges of the rails. With a small shell thickness, the bending stresses in the upper area of the sleeper decrease to 35 %, and in the lower area by 15 %. The maximum increase of up to 8 % is observed with a sharp difference in the shell thicknesses. Compressive stresses on the sleeper in the under-rail zone increase with a small shell thickness of the device due to the redistribution of forces to a smaller number of under-rail supports when the overall rigidity of the structure changes. Increasing the shell thickness to 40 cm leads to an increase in mechanical stresses of up to 20 %, which is an acceptable value with a large margin. The use of under-rail foundations with a viscous element is recommended for temporary railway tracks when laying them instead of ballast and sleepers, which allows for the track to be quickly laid and also quickly dismantled.

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.