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

作　　者：CHEN LinCong LI HaiFeng LI ZhongShen ZHU WeiQiu 

机构地区：[1]College of Civil Engineering,Huaqiao University [2]College of Mechanical Engineering and Automation,Huaqiao University [3]Department of Mechanics,State Key Laboratory of Fluid Power Transmission and Control,Zhejiang University

出　　处：《Science China(Physics,Mechanics & Astronomy)》2013年第11期2200-2207,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.10932009,11072212,11272279 and 11002059);Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103501120003);Fujian Province Natural Science Foundation of China(Grant No.2010J05006);Fundamental Research Funds for Huaqiao University(Grant No.JB-SJ1010)

摘　　要：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 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.

关 键 词：fractional derivative damping nonlinear oscillator stochastic stability Lyapunov exponent 

分 类 号：TN752[电子电信—电路与系统]