Asymptotic stability with probability one of MDOF nonlinear oscillators with fractional derivative damping

• Published in: Science China. Physics, mechanics & astronomy Vol. 56; no. 11; pp. 2200 - 2207
• Main Authors: Chen, LinCong, Li, HaiFeng, Li, ZhongShen, Zhu, WeiQiu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2013; Springer Nature B.V
• Subjects: Astronomy; Asymptotic properties; Classical and Continuum Physics; Damping; Degrees of freedom; Derivatives; Liapunov exponents; Nonlinearity; Observations and Techniques; Oscillators; Physics; Physics and Astronomy; Probability theory; Stability; Stability analysis; Stochasticity; 分数阶导数; 分数阶系统; 多自由度; 最大Lyapunov指数; 概率; 渐近稳定性; 阻尼; 非线性振荡器; fractional derivative damping; stochastic stability; nonlinear oscillator; Lyapunov exponent
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-013-5053-1

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.