磁悬浮均匀等直刚杆的非线性振动

Nonlinear Oscillation of Magnetic Levitation Uniformity Rigid Pole

采用磁悬浮技术可以解决传统控制方法在竖向隔震、微振控制等方面所面临的难题,作为这项技术应用基础研究,本文建立了磁悬浮均匀等直刚杆的运动方程,讨论了方程的稳定性,给出了随机地面扰动输入下求解非线性振动解的Runge-Kutta格式,并对悬浮刚杆在任意输入下的响应进行了分析。结果表明,系统在刚杆的静止悬浮高度附近是L稳定的,系统对随机地面输入的响应存在分岔点,只有当静止悬浮高度大于某一数值时,系统的响应才有稳定解。

The insurmountable difficulties of traditional control strategy in isolating vertical vibration and controlling micro-oscillation may be overcome by employing magnetic levitation technique. As a fundamental research of this technology, the governing equitation of rigid uniformity magnetic suspension pole is derived. The stability of the equation is studied. Runge-Kutta formula for resolving the system subjected to the random ground motion is put forward in this paper, and the responses of the pole are investigated. The results indicates that the initial suspension position of the pole is L-stable equilibrium point. Bifurcation point is existed in the response to the random ground motion, and the stable responses are presented on condition that the initial suspension heights are bigger than a certain value.