物理学报2016，Vol.65Issue(21)：210501-1-210501-6,6.DOI:10.7498/aps.65.210501
随机参激下Duffing-Rayleigh碰撞振动系统的P-分岔分析∗
P-bifurcations of a Duffing-Rayleigh vibroimpact system under sto chastic parametric excitation
摘要
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.关键词
碰撞振动系统/P-分岔/随机参激Key words
vibroimpact system/P-bifurcation/stochastic parametric excitation引用本文复制引用
徐伟,杨贵东,岳晓乐..随机参激下Duffing-Rayleigh碰撞振动系统的P-分岔分析∗[J].物理学报,2016,65(21):210501-1-210501-6,6.基金项目
国家自然科学基金(批准号:11472212,11532011,11302170)资助的课题 （批准号:11472212,11532011,11302170）
