The mathematical model of taking the account of eccentricity of a railway track on the span of railway bridges is proposed. The significant effects of the railway track eccentricity on the character of railway spans vibrations at different speeds of moving a locomotive are investigated.
The basic stages of development of the program complex for calculation of statics and dynamics of the rod and beam constructions of railway bridges based on combining the finite-element method and the equations of solid dynamics are described.
The questions of application of the Euler-Lagrange equations to the decision of forced vibration problem of system «bridge–train» are considered. The account of dynamic features of moving loading and bridge span beams are made.
The differential equations of beam motion considering of moving, elastic and dissipative forces are presented on types of oscillations and integrate longitudinal, torsional, bending as well as shearing vibrations. The basic topological structure is figured in the form of the weighed and dual graphs for determination of force and kinematic parameters. The representing algebraic system is noted as tensor relations.