Open AccessMOMENT LYAPUNOV EXPONENTS AND STOCHASTIC STABILITY OF A THIN-WALLED BEAM SUBJECTED TO AXIAL LOADS AND END MOMENTS
Author(s) -
Goran Janevski,
Predrag Kozić,
Ratko Pavlović,
Strain Posavljak
Publication year - 2021
Publication title -
facta universitatis. series: mechanical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.483
H-Index - 16
eISSN - 2335-0164
pISSN - 0354-2025
DOI - 10.22190/fume191127014j
Subject(s) - lyapunov exponent , mathematics , moment (physics) , lyapunov function , white noise , lyapunov equation , mathematical analysis , parametric statistics , monte carlo method , control theory (sociology) , statistical physics , nonlinear system , physics , classical mechanics , quantum mechanics , statistics , computer science , control (management) , artificial intelligence
In this paper, the Lyapunov exponent and moment Lyapunov exponents of two degrees-of-freedom linear systems subjected to white noise parametric excitation are investigated. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining both the almost-sure and the moment stability of a stochastic dynamic system. As an example, we study the almost-sure and moment stability of a thin-walled beam subjected to stochastic axial load and stochastically fluctuating end moments. The validity of the approximate results for moment Lyapunov exponents is checked by numerical Monte Carlo simulation method for this stochastic system.