In high-speed electric trains, a pantograph is mounted on the roof of the train to collect power through contact with an overhead catenary wire. The effect of fast harmonic and parametric excitation on a stochastically driven pantograph-catenary system is studied in this paper. A single-degree-of-freedom model of the pantograph-catenary system is adopted, wherein the stiffness of the nonlinear spring has a time-varying component characterized by both low and high frequencies. Using perturbation and harmonic averaging, a Fokker-Planck-Kolmogorov equation governing the stationary response of the pantograph-catenary system is set up. Based on the transition probability density of the stationary response, it is found that even small high-frequency parametric excitation has an appreciable effect on the system response. Among other things, it shifts the resonant frequency and often changes the response characteristics markedly. Copyright © 2014 R. H. Huan et al.

Systems which specifications change abruptly and statistically, referred to as Markovian-jump systems, are considered in this paper. An approximate method is presented to assess the asymptotic stability, with probability one, of nonlinear, multi-degree-of-freedom, Markovian-jump quasi-nonintegrable Hamiltonian systems subjected to stochastic excitations. Using stochastic averaging and linearization, an approximate formula for the largest Lyapunov exponent of the Hamiltonian equations is derived, from which necessary and sufficient conditions for asymptotic stability are obtained for different jump rules. In a Markovian-jump system with unstable operating forms, the stability conditions prescribe limitations on time spent in each unstable form so as to render the entire system asymptotically stable. The validity and utility of this approximate technique are demonstrated by a nonlinear two-degree-of-freedom oscillator that is stochastically driven and capable of Markovian jumps.

In electric trains, a pantograph is mounted on the roof of the train to collect power through contact with an overhead catenary wire. The carbon-strip suspension of a pantograph, along which contact with the catenary occurs, is subjected to harmonic and stochastic contact-force excitations. In this paper, vertical dynamics of the carbon-strip suspension is studied with an aim of improving the reliability and safety of running trains. A single-degree-of- freedom model of the carbon-strip suspension with nonlinear stiffness is developed using parameter values of the DSA X pantograph. Through stochastic averaging, a Fokker-Planck-Kolmogorov equation governing the stationary response of the carbon-strip suspension is set up. Based on the transition probability density of the stationary response, it is found that random jumps and bifurcations in the carbon-strip motion can occur. The possibility of motion bifurcations and the frequency of random jumps warrant consideration in advanced design of carbon-strip suspensions. © 2013 Springer Science+Business Media Dordrecht.