Research of the Dynamical System “Beam – Stochastic Base”

AbstractThe paper presents the methodology and algorithm for calculating the beam on the elastic base, in a probabilistic formulation taking into account dynamic forces. The basis of this method is to bring the initial load to the equivalent load, which includes deterministic and probabilistic components. The paper gives the approximating functions for symmetric and skew-symmetric components of the equivalent load under the action of a moving force. The resulting method allows to solve practical problems without use of the complicated apparatus of statistical dynamics of nonlinear systems. The reliability of the results obtained in the paper is confirmed by the use of analytical methods of calculating stochastic systems and structural dynamics, verifiable by comparing the results with the known solutions of other authors. Qualitative and quantitative correspondence with the results presented in independent sources on the subject was established