TY - JOUR

T1 - Survival probability determination of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitation

AU - Fragkoulis, Vasileios C.

AU - Kougioumtzoglou, Ioannis A.

N1 - Funding Information: The authors gratefully acknowledge the support by the German Research Foundation (Grant No. FR 4442/2-1 ).

PY - 2023/1

Y1 - 2023/1

N2 - An approximate analytical technique based on a combination of statistical linearization and stochastic averaging is developed for determining the survival probability of stochastically excited nonlinear/hysteretic oscillators with fractional derivative elements. Specifically, approximate closed form expressions are derived for the oscillator non-stationary marginal, transition, and joint response amplitude probability density functions (PDF) and, ultimately, for the time-dependent oscillator survival probability. Notably, the technique can treat a wide range of nonlinear/hysteretic response behaviors and can account even for evolutionary excitation power spectra with time-dependent frequency content. Further, the corresponding computational cost is kept at a minimum level since it relates, in essence, only to the numerical integration of a deterministic nonlinear differential equation governing approximately the evolution in time of the oscillator response variance. Overall, the developed technique can be construed as an extension of earlier efforts in the literature to account for fractional derivative terms in the equation of motion. The numerical examples include a hardening Duffing and a bilinear hysteretic nonlinear oscillators with fractional derivative terms. The accuracy degree of the technique is assessed by comparisons with pertinent Monte Carlo simulation data.

AB - An approximate analytical technique based on a combination of statistical linearization and stochastic averaging is developed for determining the survival probability of stochastically excited nonlinear/hysteretic oscillators with fractional derivative elements. Specifically, approximate closed form expressions are derived for the oscillator non-stationary marginal, transition, and joint response amplitude probability density functions (PDF) and, ultimately, for the time-dependent oscillator survival probability. Notably, the technique can treat a wide range of nonlinear/hysteretic response behaviors and can account even for evolutionary excitation power spectra with time-dependent frequency content. Further, the corresponding computational cost is kept at a minimum level since it relates, in essence, only to the numerical integration of a deterministic nonlinear differential equation governing approximately the evolution in time of the oscillator response variance. Overall, the developed technique can be construed as an extension of earlier efforts in the literature to account for fractional derivative terms in the equation of motion. The numerical examples include a hardening Duffing and a bilinear hysteretic nonlinear oscillators with fractional derivative terms. The accuracy degree of the technique is assessed by comparisons with pertinent Monte Carlo simulation data.

KW - First-passage time

KW - Fractional derivative

KW - Nonlinear system

KW - Stochastic dynamics

KW - Survival probability

UR - http://www.scopus.com/inward/record.url?scp=85145967764&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2022.103411

DO - 10.1016/j.probengmech.2022.103411

M3 - Article

AN - SCOPUS:85145967764

VL - 71

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

M1 - 103411

ER -