基于体心立方点阵力学等效的批产卫星结构设计与力学分析

doi:10.3969/j.issn.1004-132X.2026.06.015

摘要/Abstract

摘要：

针对体心立方点阵填充卫星结构仿真复杂、计算量大的问题，提出一种基于等效建模方法的解决方案。将Timoshenko梁理论和三明治理论结合，建立了点阵夹芯板的力学等效模型，并引入杆长修正参数提高模型精度。仿真与实验结果表明：在约束模态条件下，等效模型网格数量降至原模型的0.48%，前6阶固有频率最大误差不超过5.60%，且振型保持一致。卫星动力学分析进一步验证了该等效模型在整星模态分析和谐响应分析中的有效性，显著降低了建模难度与计算成本，为批量生产卫星点阵结构设计提供了可靠的技术支持。

关键词: 批产卫星, 体心立方点阵, 力学等效, 动力学分析

Abstract:

To address the challenges of high complexity and computational costs in simulating satellite structures with body-centered cubic（BCC） lattice fills，an equivalent modeling approach was proposed. A mechanics equivalent model for lattice core sandwich panels was established using Timoshenko beam theory and sandwich theory， and a strut length correction parameter was introduced to improve the accuracy. Simulation and experimental results show that under constrained modal conditions， the equivalent model reduces the number of mesh elements to 0.48% of the original， with a maximum error in the first six natural frequencies of no more than 5.60%， while maintaining consistent mode shapes. Satellite dynamic analysis further confirmed the effectiveness of the equivalent model in global modal analysis and harmonic response analysis. The method significantly reduces modeling difficulty and computational costs， and provides reliable technical support for the design of batch-produced satellite lattice structures.

Key words: batch-produced satellite, body-centered cubic lattice, mechanical equivalence, dynamic analysis

中图分类号:

TB34

王健, 石有胜, 臧国岩, 赵相禹, 董天杨, 张雷. 基于体心立方点阵力学等效的批产卫星结构设计与力学分析[J]. 中国机械工程, 2026, 37(6): 1418-1425.

WANG Jian, SHI Yousheng, ZANG Guoyan, ZHAO Xiangyu, DONG Tianyang, ZHANG Lei. Batch-producted Satellites Structural Design and Mechanics Analysis Based on Mechanics Equivalence of Body-centered Cubic Lattices[J]. China Mechanical Engineering, 2026, 37(6): 1418-1425.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.06.015

https://www.cmemo.org.cn/CN/Y2026/V37/I6/1418

图/表 20

图1 BCC点阵夹芯板结构

Fig.1 Structure of BCC lattice sandwich panel

图2 BCC点阵胞元结构

Fig.2 BCC lattice core structure

图3 BCC胞元压缩变形示意图

Fig.3 BCC unit cell compression deformation schematic diagram

图4 BCC胞元杆长重合误差原理

Fig.4 BCC unit cell strut length coincidence error principle

图5 BCC胞元剪切变形示意图

Fig.5 BCC unit cell shear deformation schematic diagram

图6 BCC芯子等效刚度

Fig.6 BCC core equivalent stiffness

表1 夹芯板等效理论

Tab.1 Sandwich panel equivalent theory

理论名称	理论特征
等效板理论	假设等效前后具有相同的弯曲刚度、平面刚度和质量
蜂窝板理论	基于哈密顿原理对夹芯板进行刚度等效和惯性等效
三明治理论	假设夹芯板由各向同性的蒙皮和正交各向异性的芯子组成

图7 BCC芯子静力学边界条件

Fig.7 Static boundary conditions for the BCC core

图8 BCC芯子静力学等效变形量及网格单元数

Fig.8 BCC core static equivalent deformation and mesh element quantity

图9 点阵芯子的力学等效相对误差对比

Fig.9 Comparison of the relative error in mechanical equivalence for the lattice core

图10 BCC夹芯板静力学边界条件

Fig.10 Static boundary conditions for the BCC sandwich panel

图11 BCC夹芯板静力学等效变形量及网格单元数

Fig.11 BCC sandwich panel static equivalent deformation and mesh element quantity

图12 BCC夹芯板的模态分析边界条件

Fig.12 Boundary conditions for the modal analysis of the BCC sandwich panel

图13 BCC夹芯板的模态分析结果

Fig.13 BCC sandwich panel modal analysis result

图14 模态实验系统构成

Fig.14 Modal experimental system composition

图15 样件自由模态实验结果

Fig.15 Specimen free modal experimental result

表2 卫星结构参数

Tab.2 Satellite structural parameter

尺寸	卫星包络/mm	胞元包络/mm
长度	770	10
宽度	535	10
高度	315	10

表3 批产卫星约束模态仿真结果

Tab.3 Batch-produced satellite natural frequency

固有频率阶数	固有频率/Hz
1	31.05
2	32.35
3	36.99
4	41.69
5	50.93
6	51.34

图16 批产卫星的约束模态振型

Fig.16 Batch-produced satellite constrained modal shape diagram

图17 批产卫星的约束模态振型图

Fig.17 Batch-produced satellite constrained modal shape diagram

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