Integration algorithm for covariance nonstationary dynamic analysis using equivalent stochastic linearization

Deterministic mechanical systems subject to stochastic dynamic actions, such as wind or earthquakes, have to be properly evaluated using a stochastic approach. For nonlinear mechanical systems it is necessary to approximate solutions using mathematical tools, as the stochastic equivalent linearizati...

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Bibliographic Details
Published in:Mathematics and computers in simulation Vol. 125; pp. 70 - 82
Main Authors: Acciani, Giuseppe, Di Modugno, Filomena, Abrescia, Angelamaria, Marano, Giuseppe C.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2016
Subjects:
Bouc–Wen mechanical model
Covariance analysis
Equivalent linearization
Lyapunov equation
Stochastic dynamics
Bouc–Wen mechanical model
Stochastic dynamics
Covariance analysis
Lyapunov equation
Equivalent linearization
ISSN:0378-4754, 1872-7166
Online Access:Get full text
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Summary:Deterministic mechanical systems subject to stochastic dynamic actions, such as wind or earthquakes, have to be properly evaluated using a stochastic approach. For nonlinear mechanical systems it is necessary to approximate solutions using mathematical tools, as the stochastic equivalent linearization. It is a simple approach from the theoretical point of view, but needs numerical techniques whose computational complexity increases in case of nonstationary excitations. In this paper a procedure to solve covariance analysis of stochastic linearized systems in the case of nonstationary excitation is proposed. The nonstationary Lyapunov differential matrix covariance equation for the linearized system is solved using a numerical algorithm which updates linearized system coefficient matrix at each step. The technique used is a predictor–corrector procedure based on backward Euler method. Accuracy and computational costs are analysed showing the efficiency of the proposed procedure.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2015.11.006