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Equivalent Linearization Methods for Stochastic Dynamic Analysis Using Linear Response Surfaces
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DOI：10.1061/(ASCE)EM.1943-7889.0001264.png)
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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 intereste.g.,first-passage probabilitiesthrough 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. (C) 2017 American Society of Civil Engineers.
Keyword:
Earthquake engineering
Equivalent linearization
First-order reliability method
Secant hyperplane method
Stochastic dynamic analysis
Tail equivalent linearization method
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5.3
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