基于广义逆矩阵的空间可展桥梁动态仿真和实验

采用广义逆矩阵方法分析空间可展桥梁的运动过程.以笛卡尔坐标系下节点的自然坐标为未知量,建立空间可展桥梁展开过程的动力学基本方程,将刚性杆长、套筒、边界约束、锁定条件、4节点等长剪刀撑、4节点刚性板的约束方程嵌入动力学方程,导出一组不含乘子且方程数等于结构自由度数的动力学方程.通过数值仿真,得出空间可展桥梁在展开过程中的各个状态及动力学参数.进行了缩比模型的研制,在电机驱动下能得到较好的控制并平稳展开,验证了该空间可展桥梁的合理性,也为空间可展桥梁的进一步研究提供了参考.

Dynamic simulation and experiment of deployable bridge based on generalized inverse matrix

The moving process of deployable bridge was analyzed with the Moore-Penrose generalized inverse matrix.Dynamic equations of deployable bridge was formulated with Cartesian coordinates of the idealized truss joint as variables.Integration of the constraint equation which includes rigid rod,socket,boundary,locking in condition,cross bracing with 4 nodes,and plane element with 4 nodes into the dynamic equations yields a group of dynamic equations with no coefficients,and the number of the equations is the same as that of freedom degree of the structure.Each state and dynamic parameter during the deploying period was obtained by numerical simulation.Scale model was designed and deployed smoothly under the control of electrical machine,which verifies rationality of this kind of bridge and provides reference value to further study of deployable bridge.