空间展开折叠桁架结构动力学分析研究

本文以笛卡尔坐标系下节点自然坐标为未知量，建立了桁架结构系的基本运动力学方程，并首次推导出桁架结构中常用节点附加几何约束方程，相应约束Jacobi矩阵及其导数矩阵，采用奇异值分解法求约束Jacobi矩阵的零空间基和M-P广义逆，并由矩阵缩减法建立了带约束桁架体系的运动力学方程和求解方法。数值算例表明该方法适于可展折叠桁架结构运动力学分析。

Dynamic analysis of deployable space truss structures

Supposed Cartersian coordinate of joint assumed as unknown variables, and dynamic equations of motion are formulated herein for deployable space truss structures. Geometric constraint equations, relevant Jacobi matrices and derivatives are developed for three classes of holonomic geometric constraint respectively. The basis of null space and M\|P generalized inverse are abtained through singular value decomposition algorithm for constraint Jacobi matrices. Using matrix reduction technique, dynamic equations of motion are thus established for constrained dynamic system. Numerical method is developed, and the algorithm proves effective for deployable truss structures.