大范围运动细长柔性空间结构动力学特性分析

自由-自由边界无约束状态的细长柔性空间结构大范围运动时的动力学特性对整体结构运动分析和运动控制系统设计具有极其重要的作用。通过浮动坐标系建立结构的运动学关系;借助假设模态法对结构变形进行变量分离;利用Lagrange’s方程建立了结构的刚柔耦合振动方程;再通过Rayleigh-Ritz法,以无大范围运动时的振型函数作为基本解组,得到了大范围运动影响下的结构振动特征方程,求解该方程得到了结构频率和振型。通过几组数值算例的对比分析,指出了非耦合模型和耦合模型下结构频率及振型之间的差异。

Dynamic characteristics analysis of slender flexible space structure undergoing large overall motions

Dynamic characteristics analysis of slender flexible space structure undergoing large overall motions is very important for the motion analysis and subsequent motion controller design.To begin with, a floating reference frame is chosen as local reference frame,whose origin is consistent with the center of mass, to establish structure's kinematic relationships; after that,the assumed mode method is used for discretizing the deformation; then,the rigid-flexible coupling vibration equations of structure undergoing large overall motions are obtained based on Lagrange's equation; next,using Rayleigh-Ritz method,the bending modes without undergoing large overall motions are selected as the basic functions to derive eigenfunction; furthermore,solving the eigenfunction to derive bending frequencies and mode shapes;finally,through several numerical examples,the difference of bending frequencies and mode shapes between uncoupling model and coupling model is discussed,and the results show that the uncoupling model is not reasonable.