关键词: 碰撞振动系统/
P-分岔/
随机参激
English Abstract
P-bifurcations of a Duffing-Rayleigh vibroimpact system under stochastic parametric excitation
Xu Wei,Yang Gui-Dong,
Yue Xiao-Le
1.Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Fund Project:Project supported by the National Natural Science Foundation of China(Grant Nos. 11472212, 11532011, 11302170).Received Date:03 June 2016
Accepted Date:25 July 2016
Published Online:05 November 2016
Abstract:Vibroimpact dynamics has been widely studied by experts and scholars in the fields of physics, engineering and mathematics. Most of the researches focus on vibroimpact systems under deterministic excitations by using numerical methods. However, random excitation often exists in vibroimpact system, whose roles cannot be neglected, sometimes may be quite important. Stochastic bifurcation is one of the most critical parts of stochastic dynamics, but the relevant researches about vibroimpact system are rarely seen so far due to the fact that the analytical method has its inherent difficulty. This paper aims to investigate the P-bifurcations of a Duffing-Rayleigh vibroimpact system under stochastic parametric excitation based on an equivalent nonlinear system method and the catastrophe theory. Firstly, the original Duffing-Rayleigh vibroimpact system is transformed into a new system without velocity jump by using the nonsmooth transformation method and Dirac function. Then, the equivalent nonlinear system method is introduced to obtain the stationary probability density of the response. Finally, the explicit parameter conditions for stochastic P-bifurcations are derived based on the catastrophe theory. Besides, the effect of stochastic parametric excitation on the system response is also discussed.
Keywords: vibroimpact system/
P-bifurcation/
stochastic parametric excitation
