Monte Carlo simulation in the stochastic analysis of non-linear systems(1).pdf

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International Journal of Non-Linear Mechanics 38 (2003) 1269–1283
Monte Carlo simulation in the stochastic analysis of non-linear
systems under external stationary Poisson white noise input
G. Muscolino ∗, G. iardi, P. iola
Dipartimento di Costruzioni e ologie Avanzate, University of Messina, Salita Sperone 31,
S. Agata, I-98166 Messina, Italy
Abstract
A method for the evaluation of the probabilitydensityfunction (.) of the response process of non-linear systemsunder
external stationaryPoisson white noise excitation is presented. The method takes advantage of the great accuracyof the
Monte Carlo simulation (MCS) in evaluating the ÿrst two moments of the response process byconsidering just few samples.
The quasi-moment neglect closure is used to close the inÿnite hierarchyof the moment di4erential equations of the response
process. Moreover, in order to determine the higher order statistical moments of the response, the second-order probabilistic
information given byMCS in conjunction with the quasi-moment neglect closure leads to a set of linear di4erential equations.
The quasi-moments up to a given order are used as partial probabilistic information on the response process in order to ÿnd
the . bymeans of the C-typeGram–Charlier series expansion.
? 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Non-linear stochastic dynamics;StationaryPoisson process; Monte Carlo simulation; Non-Gaussian probabilitydensity
function; Quasi-moment neglect closure
1. Introduction In these cases the Poisson white noise and the ÿltered
Poisson white noise processes are more realistic mod-
A broad class of random excitations on structures els [5].
can be modeled as Gaussian white noise or ÿltered Methods for the evaluation of the response of
Gaussian white noise processes. Then both analytical linear and non-linear systems under non-Gaussian
and numerical methods have been recentlydeveloped delta-correlated proces