Journal
STROJNISKI VESTNIK-JOURNAL OF MECHANICAL ENGINEERING
Volume 62, Issue 7-8, Pages 440-451Publisher
ASSOC MECHANICAL ENGINEERS TECHNICIANS SLOVENIA
DOI: 10.5545/sv-jme.2016.3752
Keywords
first-passage problem; nonlinear stochastic dynamics; evolutionary stochastic processes; nonlinear/hysteretic systems; survival probability
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Funding
- State Scholarships Foundation - IKY in Greece
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An approximate technique for assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) oscillators. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are determined. Overall, the developed technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF system exhibiting hysteresis following the Bouc-Wen model is included in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the accuracy of the technique.
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