Proceedings home preface contents authors keywords copyright reference ©2012 Civil-Comp Ltd				Paper 184 A New Method for Solving Random Vibration Problems M. Grigoriu Department of Civil and Environmental Engineering, Cornell University, Ithaca, New York, United States of America Keywords: Gaussian noise, linear systems, Monte Carlo simulation, non-Gaussian noise, nonlinear systems, random vibration, stochastic reduced order models. full paper (pdf) - reference Current random vibration methods provide efficient solutions for the second moment properties of the states of arbitrary linear systems subjected to random noise. For Gaussian noise, these properties define completely the state probability law. The random vibration methods can also be used to find the distribution of the states of simple linear systems under non-Gaussian noise and simple nonlinear systems under Gaussian or non-Gaussian noise. Monte Carlo simulation is the only general method for finding the probability laws for the states of arbitrary linear or nonlinear dynamic systems subjected to Gaussian or non-Gaussian noise. Computational effort, that can be significant when dealing with realistic systems, is the essential limitation of Monte Carlo simulation. A novel method is proposed for analysing arbitrary linear or nonlinear dynamic systems driven by Gaussian or non-Gaussian noise. The method is based on stochastic reduced order models (SROMs), that is, processes that have finite numbers of samples that may or may not be equally likely. The implementation of the method involves three steps. First, a SROM is developed for the noise process driving a dynamics system. Second, deterministic algorithms are used to calculate system responses to the samples of the input SROM. Resulting response samples define a SROM for the state of the dynamic system. Third, the SROM for the system state is used to construct approximations for response statistics. SROM-based solutions of various resolutions are used to calculate statistics for the response of a simple nonlinear dynamic system subjected to non-Gaussian noise. Response statistics are also determined for linear systems subjected to non-Gaussian noise by methods of stochastic calculus.