Clustered张拉整体结构的动力学建模  

Dynamic modeling of clustered tensegrity structures

作　　者：张子宇 王彤[1] 周斌 ZHANG Ziyu;WANG Tong;ZHOU Bin(State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Nanjing Sushi Guangbo Environmental Reliability Laboratory Co.,Ltd.,Nanjing 210016,China)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016 [2]南京苏试广博环境可靠性实验室有限公司,南京210016

出　　处：《振动与冲击》2024年第16期287-294,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(12272172)。

摘　　要：针对clustered张拉整体结构,提出了一种基于任意拉格朗日-欧拉(arbitrary Lagrangian-Eulerian, ALE)法的多体动力学模型。相较于传统的拉格朗日法模型,该研究中的模型具有更为简单的运动学约束。首先,引入了一种ALE时变长度索单元,其网格节点与物质点可以独立运动,提供了一种自然的方式描述结构中运动的滑轮和滑动绳索;其次,利用达朗贝尔原理,推导了该单元的广义力向量并计算了相应的雅可比矩阵;然后,建立了张拉整体系统的动力学方程,并利用广义α算法对其进行求解,选取节点的全局位置坐标和物质坐标作为广义坐标,其中全局位置坐标可以被不同物体共享,以减少动力学方程的自由度数和消除物体间的约束;最后,展示了一个数值算例,10层可折叠张拉整体塔架,对其折叠过程进行了准静态和动力学仿真,验证了模型的有效性。所提出的模型和算法可为clustered张拉整体结构的设计提供理论指导,具有工程意义。Aiming at clustered tensegrity structures,a multibody dynamic model was proposed based on arbitrary Lagrangian-Eulerian(ALE)method.Compared with the traditional Lagrangian model,this model has simpler kinematic constraints.First,an ALE variable length cable element was introduced.Its mesh nodes can move independently of the material points,providing a natural way to simulate the moving pulleys and the sliding cables.The generalized force vectors were derived using D'Alembert's principle,and then the associated Jacobian matrices were computed.Second,the dynamic equations of the whole tensegrity system were established,and solved using the generalized-αmethod.The global nodal position coordinates and material coordinates were selected as the generalized coordinates,in which the global nodal position coordinates can be shared by different bodies to reduce the number of DOFs of the dynamic equations,and eliminate the constraint equations between the bodies.Last,a numerical example,ten-stage tensegrity tower,was presented for both the quasi-static and dynamic deployment to verify the effectiveness of the proposed model.The model and algorithm proposed in this paper can provide theoretical guidance for the design of clustered tensegrity structures,and is of engineering significance.

关 键 词：多体动力学模型 clustered张拉整体 任意拉格朗日-欧拉(ALE) 可展开空间结构 

分 类 号：O313.7[理学—一般力学与力学基础]