超大柔性空间结构姿态振动耦合稳定性分析

Coupling Stability of Very Large Flexible Space Structures

针对太阳帆塔等细长结构的空间太阳能电站构型,以圆轨道内平面运动的空间柔性梁为研究对象,在质心浮动坐标系下,基于Hamilton原理建立了姿态运动与弯曲振动的耦合动力学模型。引入简谐形式的姿态运动假设,并验证了假设的合理性。基于此假设,分析了姿态运动与重力梯度对弯曲振动的第一阶频率的影响,重力梯度项的影响为简谐波动形式,而姿态运动使得弯曲振动频率降低,两者作用均随初始姿态角增大而增强。同时,推导了Mathieu方程形式的模态振动方程,并利用小参数摄动分析方法,得到了不同初始姿态角下的弯曲振动的稳定图,发现当初始姿态角越大时不稳定区域就越大。

Considering the slim configuration of a space solar power station like Solar Tower,the space flexible beam moving in the plane of a circular orbit is taken as the research object,and a coupling dynamic model of the attitude motion and bending vibration is established based on the Hamilton principle in the mass-centered floating coordinate system. The simple assumption of the attitude motion is introduced and its rationality of the hypothesis is verified. Based on this assumption,the influence of the attitude motion and gravity gradient on the first-order frequency of the bending vibration is analyzed. Its effect is in the form of the harmonic fluctuation： the bending vibration frequency decreases with the attitude motion and both of them are enhanced when the initial attitude angle increases. At the same time,the modal equations in the form of the Mathieu equation are deduced. By using the small parameter perturbation analysis method,the stable curves of the bending vibration under different initial attitude angles are obtained. It is shown that the larger the initial attitude angle is,the larger the unstable area is.