Equivalent Linearization Methods for Stochastic Dynamic Analysis Using Linear Response Surfaces
Publication: Journal of Engineering Mechanics
Volume 143, Issue 8
Abstract
Three methods of stochastic equivalent linearizations defined in the broad framework of structural reliability analysis are presented. These methods are (1) the Gaussian equivalent linearization method (GELM), here defined for the first time as a linear response surface in terms of normal standard random variables; (2) the tail equivalent linearization method (TELM), here reinterpreted as a stochastic critical excitation method; and (3) a novel equivalent linearization called the tail probability equivalent linearization method (TPELM). The Gaussian equivalent linear system (GELS) is the equivalent linear system (ELS) obtained by minimizing the difference between the variance of the GELS and the original nonlinear system. The tail equivalent linear system (TELS) is the ELS having the same critical excitation as the original system. The tail probability equivalent linear system (TPELS) is the ELS obtained by minimizing the difference between the tail probability of the equivalent system and the original nonlinear system. The knowledge of the ELS allows the evaluation of engineering quantities of interest—e.g., first-passage probabilities—through the application of the random vibration analysis to these systems. Shortcomings and advantages of the three methods are presented and illustrated through applications to selected representative nonlinear oscillators. Finally, the methods are applied to an inelastic multi-degree-of-freedom (MDOF) system, showing their scalability to systems of higher complexity.
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Acknowledgments
This research was funded by the Republic of Singapore’s National Research Foundation through a grant to the Berkeley Education Alliance for Research in Singapore (BEARS) for the Singapore-Berkeley Building Efficiency and Sustainability in the Tropics (SinBerBEST) Program. The authors thank Dr. S. Günay for his review of an earlier version of the manuscript and two anonymous referees who with their comments have contributed to the enhancement of the paper.
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Journal of Engineering Mechanics
Volume 143 • Issue 8 • August 2017
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©2017 American Society of Civil Engineers.
History
Received: Mar 11, 2016
Accepted: Jan 19, 2017
Published online: Apr 10, 2017
Published in print: Aug 1, 2017
Discussion open until: Sep 10, 2017
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