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The paper is devoted to the modification of the dynamic behavior model of a flat orthotropic element under shock and vibrational impacts. The impacts were caused by solid cylindrical body for the case of ballastless railway construction. The suggested model allows simulating the element deformation in the upper structure of the ballast-free design track. The propagation of elastic waves moving with finite speeds, orthotropic properties of the foundation slab, which allow optimally selecting rod reinforcement are taken into account. The obtained analytical and graphical results make it possible to assess the influence of properties of the reinforced concrete slab, the underframe speed, the presence of defects in wheel sets or rail bars, as well as the characteristics of the technical content of the track section.

The paper presents a mathematical model for behaviour of a rail string segment bound by several railway sleepers. The model makes it possible to account for prestressing due to joining rail sections into a string, for anisotropic properties of the rail-and-sleeper assembly, and effects caused by the rolling stock for various initial loading conditions. We considered eleven functions describing wheel--rail contact. These functions enable us to select the most accurate model to describe the effects that vehicles have on railway segments that may differ in design specifics, mechanical properties of materials used, operation modes, and the presence of flaws on the rail tread and wheelset tread. The wave equations used to describe the behaviour of a rail string segment can simulate the process of elastic wave propagation after wheelset contact takes place, which is considerable in the case of high vehicle velocities. The investigation conducted allowed us to plot the wheel--rail interaction force for various contact models. The functions specified make it possible to select the optimum force ratio, taking into account the following: geometrical, mechanical and design parameters of the railway segment; operation modes; and the functions sought for in terms of obtaining the desired maximum contact force, contact duration, and loading and relief times