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In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the system.As an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of system.In particular,the case of factional order more than 1 is studied for the first time.
In this paper, the asymptotic stability with probability one of multi-degree-of-freedom (MDOF) nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated. A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent, whose sign determines the stability of the system. As a two-coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of the system. In particular, the case of factional order more than 1 is studied for the first time.