Stochastic stability and stochastic bifurcation of a rotor-box system with time delay and rubbing impact
In this paper,we study the stochastic stability and stochastic bifurcation of a rotor-box system with time-delay and rubbing impact.Considering that there exists time-delay from receiving signal to processing signal as well as the stochastic fluctuation of external environment,we establish a stochastic and infinite-dimensional dynamical system with time delay.First,the dynamical system is transformed into a finite-dimensional stochastic differential equation by using the central manifold method,the corresponding Itô equa-tion for the response amplitude of equation is deduced by using the stochastic averaging method.Second,The Itô equation is analyzed by using the Lyapunov exponential method and the singular boundary theory,condi-tions for the stochastic stability and stochastic bifurcation of the equation are obtained,and the joint probabil-ity density function is deduced.Finally,numerical simulation for the joint probability density function are implemented to explore the stochastic bifurcation of system.It is shown that either the time delay or the rub-bing impact coefficient can result in the stochastic P-bifurcation of system with exactly opposite effect.On the one hand,with the increasing of time delay,the P-bifurcation phenomenon of system gets more and more ob-vious,which means that the stability of system is weakened.On the other hand,with the increasing of rub-bing impact coefficient,the system becomes more and more stable.The obtained result is expected to help the design,operation and remaining life assessment of rotating machinery.
国家科技期刊平台
NSTL
万方数据
