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 引用本文: 李元恒, 范瑞祥, 杨帆, 张宏剑, 吴会强. 基于线性等效模型的堆叠式多星组合体模态分析. 力学学报, 2024, 56(8): 2364-2380.
Li Yuanheng, Fan Ruixiang, Yang Fan, Zhang Hongjian, Wu Huiqiang. Modal analysis of multi-satellite stack based on linear equivalent model. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(8): 2364-2380.
 Citation: Li Yuanheng, Fan Ruixiang, Yang Fan, Zhang Hongjian, Wu Huiqiang. Modal analysis of multi-satellite stack based on linear equivalent model. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(8): 2364-2380.

## MODAL ANALYSIS OF MULTI-SATELLITE STACK BASED ON LINEAR EQUIVALENT MODEL

• 摘要: 堆叠式多星组合体是一种新型的一箭多星发射结构布局形式. 多星组合体中的卫星采用平板构型, 平板卫星上下相邻两层支脚相互接触, 并由连接杆施加预紧力将其整体压紧. 针对这种连接形式的多星组合体结构, 文章提出了一种建立其线性等效力学模型的方法, 并开展了模态分析. 根据组合体中子结构形式及其受力特点, 分别将连接杆等效为受轴向预紧力作用的欧拉-伯努利梁模型, 以及将中间卫星连接体等效为附加集中质量点的铁木辛柯梁模型, 分别求取了二者在固定时刻随轴向坐标变化的振型函数. 通过将连接杆和卫星连接体等效模型振型函数联立求取了组合梁整体的振型函数, 并根据并联U型梁边界协调原理确定的约束条件, 求取了组合梁振动的频率特征方程. 通过将组合体有限元模型求解结果与理论模型求解结果进行对比, 验证了理论模型的正确性. 此外, 探究了预紧力、连接杆材料、支脚材料和有效载荷质量对组合体振动特性的影响规律. 提出的等效方法, 可为堆叠式多星组合体结构设计以及刚度匹配要求提供相应的指导.

Abstract: Multi-satellite stack is a new type of multi-satellite launching structure layout. The satellites in the stack adopt a flat plate configuration, where the upper and lower abutment of the flat plate satellite contact each other and are compressed as a whole by connecting rods. This article establishes a linear equivalent mechanical model and conducts modal analysis of this type of connected multi-satellite stack structure. Based on the substructure form and force characteristics of each part in the stack, the connecting rod is equivalent to an Euler Bernoulli beam model subjected to axial preload, and the intermediate satellite bonding body is equivalent to an additional lumped mass in the Timoshenko beam model. The vibration mode functions of the two with respect to axial coordinate at a fixed time are calculated. By combining vibration mode functions of the equivalent model of the connecting rod and satellite bonding body, the overall vibration mode function of the composite beam is obtained. Based on the constraint conditions determined by the parallel U-beam boundary coordination principle, the frequency characteristic equation of the composite beam vibration is obtained. The correctness of the theoretical model is verified by comparing the solution results of the finite element model with the solution results of the theoretical model. The influence of preloading force, connecting rod material, support foot material, and effective load mass on the vibration characteristics of stack is explored with conclusions. Through the equivalent method proposed in this article, corresponding guidance can be provided for the structural design and stiffness matching requirements of multi-satellite stack structure in the future.

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