基于Timoshenko梁模型的旋转弹箭横向振动模态分析

Modal Analysis of Transverse Vibration of a Spinning Rocket Based on Timoshenko Beam

将旋转弹箭简化为Timoshenko旋转梁,基于有限单元法研究了其在自由飞行时的横向振动模态.采用Timoshenko梁模型,考虑陀螺效应和剪切效应,运用转子动力学和有限单元法的思想,建立旋转弹箭横向振动的有限元方程和频率方程.利用该频率方程,分别采用Rayleigh梁和Timoshenko梁模型对某旋转弹箭进行模态分析,对不同梁模型下的横向振动进动频率进行对比,并讨论弹箭转速和长径比对模态频率的影响.

The spinning rocket is simply modeled as a Timoshenko rotor. The natural modal of transverse vibration of spinning rocket in free flight is studied based on finite element method. Under consideration of gyro-effect and shear effect, finite element equation and frequency equation of transverse vibration of the spinning rocket are both presented based on Timoshenko beam model and theory of rotor dynamics. With the aid of presented frequency equation, modal analysis of a certain rocket could be made by adopting Rayleigh beam and Timoshenko beam model separately. Further, precession frequencies of transverse vibration of the rocket for different beam models have been contrasted and the discussion about the effects of rotate speed and slenderness ratio of the rocket on the inherent characteristics has been done.