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Shock and Vibration
Volume 2014, Article ID 792673, 8 pages
Research Article

The Effect of High-Frequency Parametric Excitation on a Stochastically Driven Pantograph-Catenary System

1Department of Mechanics, Zhejiang University, Hangzhou 310027, China
2Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
3Department of Civil Engineering, Xiamen University, Xiamen 361005, China

Received 5 June 2013; Accepted 7 August 2013; Published 11 February 2014

Academic Editor: Reza Jazar

Copyright © 2014 R. H. Huan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.