变速旋转梁的建模与运动稳定性分析

利用哈密顿原理建立了支承运动情况下变速旋转梁的弹性振动方程及边界条件。根据模态分析方法，利用边界条件以及模态函数的性质，得到了一组惯性解耦时变系数的模态坐标方程组。并分析了几种特殊情况下的经典时变振动方程即Hill方程和Mathieu方程。将时变系数的常微分方程组变为增量形式，根据Newmark方法逐步积分，运用梁端部弹性振动的相轨迹分析了该时变系统的稳定性。最后给出了变角速度情况下，常有支承运动旋转梁的稳定性分析算例。

Vibration of Rotating Beam with Varying Angular Velocity and Subjected to Base Excitation

The dynamic equation and boundary condition of the rotating flexible beam carrying a concentrated mass at its free end ware derived. The rotating beam with a varying angular velocity undergoes a vertical base excitation and a horizontal base excitation. By using Assumed Mode Approach and the boundary condition, the mode coordinate equation with time variation coefficient and inertia uncoupling was analyzed. Finally, The stability was investigated according to the phase trajectory.This study also aimed at investigating the influence of the varying angular velocity on the stability of the response.A numerical example is given to demonstrate the effectiveness of the proposed study.