剪式单元阵列可展结构的动力学分析方法

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (9) : 56-60.

论文

剪式单元阵列可展结构的动力学分析方法

彭麒安，王三民，智常建，李博

作者信息 +

Dynamic analysis method for a planar linear array deployable structure with scissor-like elements

PENG Qi’an, WANG Sanmin, ZHI Changjian, LI Bo

Author information +

文章历史 +

摘要

随着阵列单元数目增多，用传统有限元动力学分析方法分析阵列可展结构计算量十分巨大，甚至变得不可能。依据阵列可展结构由单元机构规律性组合而成的特点，针对剪式单元阵列可展结构提出了一种规范化动力学分析方法（简称规范法）。此方法将单元机构的叠加节点自由度与内部节点自由度分开，从而实现单元特性矩阵的首尾循环相加得到整体结构的刚度矩阵和质量矩阵。以55剪式单元平面阵列可展结构为例，采用规范法分析其固有频率和动态响应情况。结果发现：当展开角度接近于0°和180°时，固有频率迅速减小至0 Hz。当施加外载时，无阻尼、小阻尼和过阻尼情况下的动态响应分别为周期性振动、最大振幅衰减的周期性振动和无振动。可以得出：可展结构在0°和180°附近结构不稳定，其安全工作角度为20°到160°之间。阻尼适当增大可以有效减小振动。规范法提高了建模效率，并且便于规范性编程计算。

Abstract

With increase in array elements, the computation amount to analyze an array deployable structure is huge based on the conventional FEM dynamic analysis method, even the computation becomes impossible. The specification dynamic method (SDM) for a planar linear array deployable structure with scissor-like elements was proposed according to its feature of it being regularly composed of element mechanisms. The superposition node DOFs among element mechanisms and internal node DOFs were separated with this method to realize element characteristic matrices added end to end circularly, and obtain the global stiffness matrix and mass one of an array deployable structure. Taking a 55 planar linear array deployable structure with scissor-like elements as an example, its natural frequencies and dynamic responses were analyzed with the SDM. The results showed that the structure’s natural frequency decreases to 0 Hz rapidly when its deployable angle is close to 0 or 180; when external loads are applied, the dynamic responses of the system are periodic vibration, periodic vibration with the maximum amplitude attenuated, and no vibration, respectively under undamped, underdamped and overdamped conditions; the structure with the deployable angle close to 0 or 180 is unstable, the safe range of the deployable angle should be 20 to 160; in addition, appropriately increasing damping can reduce the structure’s vibration effectively; the SDM can be used to improve modeling efficiency, and it is easy to be regularly programmed for computation.

导出引用

彭麒安，王三民，智常建，李博. 剪式单元阵列可展结构的动力学分析方法[J]. 振动与冲击, 2018, 37(9): 56-60

PENG Qi’an, WANG Sanmin, ZHI Changjian, LI Bo. Dynamic analysis method for a planar linear array deployable structure with scissor-like elements[J]. Journal of Vibration and Shock, 2018, 37(9): 56-60

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