MOMENT LYAPUNOV EXPONENTS AND STOCHASTIC STABILITY OF A THIN-WALLED BEAM SUBJECTED TO AXIAL LOADS AND END MOMENTS

Y 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.

Automated summary

This paper investigates the Lyapunov exponent and moment Lyapunov exponents of two degrees-of-freedom linear systems subjected to white noise parametric excitation. The study aims to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises and their importance in determining the almost-sure and moment stability of a stochastic dynamic system. As an example, the almost-sure and moment stability of a thin-walled beam subjected to stochastic axial load and stochastically fluctuating end moments is studied, and the validity of the approximate results for moment Lyapunov exponents is checked through numerical Monte Carlo simulation method.