Moment Lyapunov exponents and stochastic stability of a double-beam system under compressive axial loading

Abstract

a b s t r a c tThe 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 the almost-sure and moment stability of a stochastic dynamical system. As an example, we study the almost-sure and moment stability of the double-beam system under stochastic compressive axial loading. The validity of the approximate results for moment Lyapunov exponents is checked by the numerical Monte Carlo simulation method for this stochastic system.

Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise

“…If viscoelasticity is not considered, that is, = 0 and = , and the noise is taken as a white noise, that is, (2 1 ) = (2 2 ) = ( ± ) = ( ∓ ), then (42) is reduced to the moment Lyapunov exponent for 2DOF linear systems subjected to white noise parametric excitation, reported in (3.19) in [5], where a perturbation method was applied. The moment stability boundary is then obtained as …”

“…For 2DOF coupled systems, however, relatively fewer studies can be found in the literature [4,5]. The reason is that the computational process is much more complicated even if only one more degree is considered, especially in the case when the viscoelasticity is involved.…”

Dynamic stability and instability of a double-beam system subjected to random forces

“…Using the Lyapunov exponent and moment Lyapunov exponent, Kozić et al [13] obtained the almost-sure stability condition when f 1 (t)¼f 2 (t)¼e 1/2 x(t). Here, we will study the case when these processes are not identical.…”

“…When studying the equation for a single axially loaded beam, numerical difficulties arise in the determination of natural frequencies due to the presence of exponentially large terms, as is noted by Williams [12]. Stochastic stability of a double-beam system subjected to small intensity white noise excitation is investigated by Kozić et al [13].…”

Moment Lyapunov Exponents and Stochastic Stability of a Three-Dimensional System on Elastic Foundation Using a Perturbation Approach

“…Khasminskii and Moshchuk [12] obtained an asymptotic expansion of the moment Lyapunov exponents of a two-dimensional system under white noise parametric excitation in terms of the small fluctuation parameter e, from which the stability index was obtained. Kozic et al [13] investigated the Lyapunov exponent and moment Lyapunov exponent of a double-beam system without connected damping coefflcient fluctuated by white noise considered as a separate viscosity system. The method of regular perturbation was used to obtain explicit expressions for these exponents in the presence of small intensity noises.…”