A conditional Galerkin - RBF - perturbation approach for the stochastic dynamics of uncertain systems

This paper presents a Hybrid Radial Basis Functions / Galerkin Perturbation (GRBF) approach for the dynamics analysis of mechanical systems affected by randomness both in parameters and loads. In specialized literature various procedures are nowadays available in order to evaluate the response statistics of such systems, but a choice has to be made sometimes between simpler methods (that provide often unreliable solutions) and more complex methods (where accurate solutions are provided by means of a heavy computational effort). The proposed method, which is still under testing, combines a Radial Basis Functions (RBF) based Galerkin method with a perturbation approach, originally due to Liu, Belytschko & Mani, for the approximation of the system response. In order to keep as low as possible the number of differential equation to be solved a Karhunen – Loeve expansion for the excitation is used A numerical solution for a non-linear single degree of freedom (SDOF) system with random parameters is introduced, and compared with the results given by Monte Carlo Simulation (MCS) so as to provide the validation of the proposed approach. The proposed method, which is still under testing, could be a valid alternative to the classical procedures because it seems able to provide very good approximations.