Rayleigh旋转梁的动力学建模与动态稳定性分析

Modeling and dynamic stability analysis of spinning Rayleigh beams

基于Rayleigh梁理论,通过欧拉角,运用Hamilton原理,建立了柔性自转轴在Euler坐标系下和Lagrange坐标系下的动力学方程,两个方程相比,Euler坐标系下的动力学方程增加了一个离心力项。运用Galerkin方法对两组方程离散,运用Matlab的数值方法求解了系统的频率和模态。由模态分析得出,离心力项会使陀螺系统的模态在一定转速下由反进动转变为正进动模态;由稳定性分析得出,当转速足够大时,离心力项会使陀螺系统发生颤振失稳现象。

Based on the Rayleigh beam theory and using the Euler angle and the principle of Hamilton, the dynamic equations of the flexible rotation axis under the Euler coordinate system and the Lagrange coordinate are established. In comparison with the two equations, a centrifugal force term is added to the dynamic equation in the Euler coordinate system. The Galerkin method is used to discretize the two sets of equations. The frequency and mode of the system are solved by using the numerical commercial code of Matlab. From modal analysis, it is concluded that the centrifugal force makes the gyro system change from the reverse precession to the forward precession mode at a certain speed, and the stability analysis shows that when the speed is large enough, the centrifugal force will cause the flutter instability of the gyro system.