A probabilistic estimate of the vertical dynamic forces acting on the track, in the model of a three-layer beam under the influence of a four-axle freight car

The article contains a method for determining the ma-the permanent way as deflections, angles of section rotation, bending trix of mutual spectral densities of vertical dynamic forces acting on a moments, transverse forces, stresses of its three-layer structures. railway track, depending on its spectrum of irregularities. It will allow to Mathematical model of track oscillations is used for calculations make a more accurate calculation of the mean values and mean-square as a construction containing three infinitely long beams, the lower deviations of vertical dynamic forces, as well as such characteristics of of which lies on the modified Winkler base. Authors present formulas for finding amplitude-frequency characteristics connecting vertical deflections of structural layers and vertical dynamic load acting on a track. A method is described for finding a matrix of mutual spectral densities of vertical dynamic forces acting on a track having real deviations from its position in the profile, with the passage through it of a four-axle freight car. Considered example finds the amplitude-frequency characteristic that connects the vector of dynamic forces in the contacts of wheels and rails with the vector of vertical displacements of wheel centers for the model of a four-axle car. Concluding authors give the results of calculations of the amplitude-frequency characteristic of the elements of the matrix of mutual spectral densities of vertical dynamic forces acting on the track. The received statistical estimations can be used at calculations of service life of ballastless track constructions and loading on roadbed.