An effective method for the evaluation of the pdf response of dynamic systems subjected to non-stationary loads

This paper deals with the evaluation of the response probability density function (pdf) and/or characteristic function (cf) of linear systems subject to stochastic loads. It proposes a new method based on the new version of Probabilistic Transformation Method (PTM). An important aspect of the proposed approach is the ability to join directly the pdf of the input load with that of the response. Working in term of pdfs and/or cfs, the stochastic properties of the response process are full described. This enables to take into account the non Gaussianity and non stationarity of the process. Based on the step-by-step integration method, explicit solutions will be proposed for the random response of systems driven by loads stochastically defined by their cf or loads defined by a quadratic relation of a Gaussian process.