An evolutive probability transformation method for the dynamic stochastic analysis of structures

Abstract

The problem of the stochastic response determination of dynamic systems, once the random properties of the actions are assigned, is studied. In the present work, an extension of the Probability Transformation Method (PTM) to the dynamic systems has been proposed. In particular, an evolutive PTM (EPTM) is introduced. Based on the properties of the mean square random calculus with the principle of conservation of probability, the EPTM applies the PTM contextually to the mean square Riemann integral of the system solution process. In this way, the EPTM gives the expression of the single-time evolutive characteristic function (CF) of the system’s output. The application to a linear structural systems subject to assigned stochastic process excitations and random initial conditions has revealed the efficiency of the stochastic procedure.