TY - JOUR

T1 - Nonlinear MDOF system survival probability determination subject to evolutionary stochastic excitation

AU - Mitseas, Ioannis P.

AU - Kougioumtzoglou, Ioannis A.

AU - Spanos, Pol D.

AU - Beer, Michael

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Evolutionary stochastic processes

KW - First-passage problem

KW - Nonlinear stochastic dynamics

KW - Nonlinear/hysteretic systems

KW - Survival probability

UR - http://www.scopus.com/inward/record.url?scp=84979498511&partnerID=8YFLogxK

U2 - 10.5545/sv-jme.2016.3752

DO - 10.5545/sv-jme.2016.3752

M3 - Article

AN - SCOPUS:84979498511

VL - 62

SP - 440

EP - 451

JO - Strojniski Vestnik/Journal of Mechanical Engineering

JF - Strojniski Vestnik/Journal of Mechanical Engineering

SN - 0039-2480

IS - 7-8

ER -