Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 213094, 30 pages
Research Article

A Hybrid Approach for the Random Dynamics of Uncertain Systems under Stochastic Loading

Department of Civil and Environmental Engineering (DICeA), University of Florence, Street Santa Marta 3, 50139 Florence, Italy

Received 10 June 2010; Revised 23 December 2010; Accepted 15 February 2011

Academic Editor: Oded Gottlieb

Copyright © 2011 Michele Betti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a hybrid Galerkin/perturbation approach based on Radial Basis Functions for the dynamic analysis of mechanical systems affected by randomness both in their parameters and loads. In specialized literature various procedures are nowadays available to evaluate the response statistics of such systems, but sometimes a choice has to be made between simpler methods (that could provide unreliable solutions) and more complex methods (where accurate solutions are provided by means of a heavy computational effort). The proposed method combines a Radial Basis Functions (RBF) based Galerkin method with a perturbation approach for the approximation of the system response. In order to keep the number of differential equations to be solved as low as possible, a Karhunen-Loève (KL) expansion for the excitation is used. As case study a non-linear single degree of freedom (SDOF) system with random parameters subjected to a stochastic windtype load is analyzed and discussed in detail; obtained numerical solutions are compared with the results given by Monte Carlo Simulation (MCS) to provide a validation of the proposed approach. The proposed method could be a valid alternative to the classical procedures as it is able to provide satisfactory approximations of the system response.