Uncertain nonlinear dynamical systems subjected to seismic loads

This paper deals with the transient response of a nonlinear dynamical system with random uncertainties and subjected to earthquake. The nonparametric probabilistic model of random uncertainties recently published and extended to nonlinear dynamical system analysis is used in order to model random uncertainties related to the linear part of the finite element model. The nonlinearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints defined by the available information allow the probabilistic model of such random variables to be constructed. Therefore, a nonparametric-parametric formulation is developed in order to model all the sources of uncertainties in such a nonlinear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed and concerned a reactor coolant system under seismic loads.