Stochastic analysis of vibrations of tall buildings under random perturbations of the foundations

In this paper, a model of a vertical column is used to analyze the random oscillations of multi-storey buildings excited by unsteady horizontal and vertical foundation accelerations. The displacement of the column is described by a linear parametric stochastic partial differential equation. Using the concept of the probability density functional, partial differential equations for the functions of the mathematical expectation and covariances are obtained for motions of the column.