Statistical Model for Dynamic Analysis of Beams on Stochastic Foundation

The solution is found for a part of a complex problem - a choice of a calculated scheme of a model “beam - stochastic foundation”. A random field of physic-mechanical characteristics of the foundation is accepted in the form of a sum of a trend and a random variable, considering macro and microheterogeneity. The basic model is evaluated for linearity of a stochastically non-linear differential equation. The principles of constructing an equivalent model “beam - stochastic foundation” are provided. They're based on setting the initial load to an equivalent one, which includes determined and probable variables. The given model can be used to find an approximate solution to the problem of beam oscillation in a linearly deformed half-space, in a determined or random setting. Unlike other estimated models, this one takes into consideration not only the impact of heterogeneous properties of mechanical parameters of the foundation, but it also can be used with regard to heterogeneity of any nature.