中国空间科学技术

中国空间科学技术

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空间张拉薄膜应力补偿法与自由振动分析

张文尧1,2，史创1,2，郭宏伟1,2，刘荣强1,2,*
  

  1. 1.哈尔滨工业大学机电工程学院，哈尔滨150000
    2.宇航空间机构全国重点实验室，哈尔滨150000
  • 收稿日期:2025-05-16 修回日期:2025-09-09 录用日期:2025-09-15 发布日期:2026-04-09

Stress compensation method for spatial tension membranes and free vibration analysis

ZHANG Wenyao1,2，SHI Chuang1,2，GUO Hongwei1,2，LIU Rongqiang1,2,*   

  1. 1.School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150000, China
    2.National Key Laboratory of Aerospace Institutions, Harbin 150000, China
  • Received:2025-05-16 Revision received:2025-09-09 Accepted:2025-09-15 Online:2026-04-09

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摘要： 柔性太阳翼、薄膜天线等以张拉薄膜为核心部件的航天结构对应力变化高度敏感，在压缩载荷下容易出现褶皱。为构建更为精确的应力场解析模型，提出了一种基于叠加原理的用于精确分析角点张拉薄膜的自由振动的应力补偿法。首先基于由集中力引起的径向应力分布模型，建立了角点张拉薄膜的初始应力场模型。依据角点张拉薄膜的边界自由的特点，提出了通过在薄膜边界施加与初始应力场模型边界法向应力等值反向的虚拟外部载荷对初始应力场进行补偿修正的方法。在综合考虑膜的几何刚度、网格生成策略及空气附加质量的基础上，建立了张拉方形薄膜的自由振动模型，并通过将应力补偿法的计算结果与有限元仿真数据及NASA公布的实验报告进行对比验证模型的有效性。结果表明，通过应力补偿法获得的中心点第一主应力和第二主应力相较基准有限元结果的相对误差分别为0.93%与2.15%，表明应力构建精度较高。在模态分析方面，第1阶固有频率的理论计算值相对实验测量值的误差为4.6%，具有良好的准确性；在高阶频率中，如第5阶，理论计算的误差为27.7%，仍能保持较好的一致性，进一步验证了该方法在多阶振动预测中的有效性与适用性。综上所述，应力补偿法可有效构建物理合理的初始应力场，其应力场分布平滑且边界过渡自然，显著提升了模态分析的准确性，具有良好的工程实用性与推广价值。可为柔性太阳翼和薄膜天线等航天结构的设计与动态性能预测提供可靠的理论支持与技术支撑。

关键词: 张拉薄膜, 应力补偿法, 预皱分析, 应力分布, 自由振动

Abstract: Flexible solar arrays and membrane antennas, as typical aerospace structures utilizing tensioned membranes, are highly sensitive to stress variations and prone to wrinkling under compressive loads. To improve the accuracy of analytical stress field modeling, a stress compensation approach based on the principle of superposition is proposed for the free vibration analysis of corner-tensioned membranes.A radial stress distribution model induced by a concentrated force was first employed to construct the initial stress field. Considering the free-boundary characteristics of corner-tensioned membranes, a virtual boundary loading scheme was introduced to compensate the initial stress by applying external loads equal in magnitude and opposite in direction to the normal boundary stress. A vibration model of a square tensioned membrane was developed by incorporating geometric stiffness, mesh generation strategies, and the effect of added air mass. The effectiveness of the proposed method was verified through comparison with finite element simulations and NASA-released experimental data.The calculated first and second principal stresses at the membrane center showed relative errors of 0.93% and 2.15%, respectively, when compared to finite element references. For modal analysis, the theoretical first natural frequency deviated by only 4.6% from experimental results, while the fifth mode exhibited a deviation of 27.7%, confirming the method’s effectiveness in predicting multiple vibration modes with good accuracy.The proposed stress compensation method accurately reconstructs a physically realistic stress field with smooth distribution and natural boundary transitions. It significantly improves the precision of modal predictions and shows strong potential for engineering applications. The method offers a reliable theoretical basis and practical tool for the design and dynamic analysis of flexible aerospace membrane structures.

Key words: tensioned membranes, stress compensation method, prewrinkling analysis, stress distribution, free vibration