Fragkoulis, Vasileios C 
ORCID: 0000-0001-9925-9167 and Kougioumtzoglou, Ioannis A
(2023)
Survival probability determination of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitation.
PROBABILISTIC ENGINEERING MECHANICS, 71.
p. 103411.
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Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | First-passage time, Fractional derivative, Nonlinear system, Stochastic dynamics, Survival probability |
| Divisions: | Faculty of Science and Engineering > School of Engineering |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 07 Aug 2023 15:53 |
| Last Modified: | 05 Jan 2024 02:30 |
| DOI: | 10.1016/j.probengmech.2022.103411 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3172082 |
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