参数激励下受电弓系统的分岔与混沌

Bifurcation and Chaos of A Pantograph System under Parametric Excitation

以速度平方阻尼力来表示受电弓框架的液压减振器所产生的非线性阻尼力,以变刚度的弹簧系统模拟接触网,建立了受电弓系统的非线性动力学模型。利用Hopf分岔定理找到受电弓产生Hopf分岔必须满足的参数条件,采用数值积分方法,对由于速度变化及参数激励导致的非线性动力学行为进行了研究,揭示了该系统由倍周期分叉、拟周期运动,通向混沌现象,研究结果为进一步研制国产高速受电弓提供了理论参考。

Nonlinear dynamical model of a pantograph system is built, in which a square velocity damping force is used to describe the nonlinear damping force of the hydraulic vibration damper, and the catenary system is modeled by a spring of alterable stiffness. The necessary parameter condition for the Hopf bifurcation to take place in the pantograph system is obtained. This paper also presents the investigation of the dynamical behavior of the pantograph due to velocity changing and parametric excitation.The period doubling bifurcation, quasi-periodical bifurcation and chaos are revealed in the system. The investigation offers theoretical reference for the design of high-speed pantograph system.