Forced Vibrations of a Finite-Length Beam on a Stochastic Elastic Foundation under Stationary Random Loading

Abstract

In this paper, an algorithm is presented for the analysis of beams resting on a two-parameter Vlasov–Pasternak foundation under forced vibrations. The external vibrational load and the foundation (subgrade reaction) coefficients are modeled as Gaussian stationary random functions of the beam coordinate. To compute the mean values and standard deviations of deflections at the beam cross-sections, the generalized Bubnov-Galerkin method is employed, followed by Monte Carlo statistical simulation in the MATLAB environment. Based on the proposed algorithm, diagrams of the mean values and standard deviations of the beam deflections are constructed for various probability distributions of the input coefficients in the Monte Carlo method, with the first two moments kept fixed. It is shown that, for practical design, the use of Student’s t and Laplace distributions instead of the normal distribution to evaluate the statistical characteristics of beam deflections is more appropriate, since it
makes it possible to account for the possibility of extremely rare yet significant exceedances of deflections under conditions of limited experimental data, strongly heterogeneous soil regions, and insufficient knowledge of the foundation.