Moment stability of viscoelastic system influenced by non-Gaussian colored noise

Abstract This paper investigates moment stability of the plate with viscoelasticity, and determinates the expressions of pth moment Lyapunov exponents, for a finite value of p. Although, both are the significant indexes to study stochastic stability, in comparison with maximum Lyapunov exponent, moment Lyapunov exponent is more considerable and is more difficult to evaluate. In this paper, we take a non-Gaussian colored noise as the excitation of the system. Applying stochastic averaging method and the technique proposed by Larionov, the coupled equations governing the motion of the system are converted to the Ito differential equations, through which the pth moment Lyapunov exponents are conveniently evaluated, and then, the largest Lyapunov exponents are given by its relationship with the moment Lyapunov exponents. The stability boundaries, which indicate the transition state, and stability indexes of the system, which represents the probability for an almost surely stable system exceeds a threshold, are then discussed in detail. Via the numerical simulation, it is shown that the analytical expressions of moment Lyapunov exponents agree well with numerical results. At last, the effects of both noise parameter and system ones on moment Lyapunov exponents are studied, from which quantitative analysis for the practical systems with viscoelasticity can be supplied.

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