大型复杂航天器刚-液-柔耦合动力学研究

闫森; 岳宝增; 马伯乐

doi:10.21656/1000-0887.460040

大型复杂航天器刚-液-柔耦合动力学研究

doi: 10.21656/1000-0887.460040

北京理工大学宇航学院, 北京 100081

基金项目:

国家自然科学基金(重点项目) 12132002

详细信息

作者简介:
闫森(1997—)，男，硕士(E-mail: 919786111@qq.com)

通讯作者:
岳宝增(1962—)，男，教授，博士(通信作者. E-mail: bzyue@bit.edu.cn)

中图分类号: O31
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- 文章访问数: 72
- HTML全文浏览量: 22
- PDF下载量: 13
- 被引次数: 0
出版历程
- 收稿日期: 2025-03-03
- 修回日期: 2025-12-16
- 刊出日期: 2026-03-01

Coupling Dynamics Research of Large Complex Rigid-Liquid-Flexible Spacecrafts

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, P.R.China

摘要

摘要: 新一代航天器通常需要携带复杂的大尺寸柔性太阳帆板和大容量的液体燃料贮箱，以完成长时间及复杂的在轨飞行任务. 航天器在机动和控制过程中会产生刚体运动、液体晃动及柔性附件振动之间的非线性耦合问题. 该文基于Kirchhoff-Love板理论和有限元分析方法计算了柔性帆板振动，采用势函数理论计算了液体燃料晃动，借助Lagrange方法推导出刚-液-柔耦合系统的动力学模型，揭示了主刚体运动、液体晃动和柔性附件振动之间的耦合动力学特性. 通过与已发表的实验和分析结果的比较，验证了所提出的刚-液-柔耦合航天器建模方法的有效性. 考虑含有复杂大尺寸柔性太阳帆板的充液航天器耦合分析结果表明，有限元方法能够准确描述柔性附件高频模态的动态响应. 同时，由于该类大型复杂空间结构部件的低频特性，与液体燃料晃动的耦合问题也更加突出.
- 液体晃动 /
- 复杂柔性附件 /
- 有限元方法 /
- 刚-液-柔耦合
Abstract: To accomplish long-duration and complex orbit flight missions, next-generation spacecrafts need to carry large flexible structures and high-capacity liquid fuel tanks. The nonlinear coupling problems between rigid body motion, liquid sloshing, and flexible structure vibrations become particularly significant during spacecraft maneuvering and control processes. A dynamic model for rigid-liquid-flexible coupling systems was presented, to first calculate the vibration of the flexible structure with the Kirchhoff-Love plate theory and the finite element methods. Then the flow theory was employed to model liquid fuel sloshing, and finally the overall dynamic model for the coupling system was derived with the Lagrange method. The study reveals the coupling dynamic interactions between rigid body motion, liquid sloshing, and flexible structure vibrations. The proposed modeling approach for rigid-liquid-flexible coupling spacecrafts was validated by comparison with published experimental and analytical results. The coupling analysis of complex, liquid-filled spacecrafts with large, flexible structures shows that, the finite element method can accurately capture the dynamic responses of high-frequency modes of the flexible structures. Additionally, due to the low-frequency characteristics of these large and complex space structures, the coupling effects with liquid fuel sloshing become even more pronounced.
- liquid sloshing /
- complex flexible structure /
- finite element method /
- rigid-liquid-flexible coupling

HTML全文

图 1 刚-液-柔耦合航天器坐标系示意图

Figure 1. Schematic diagram of the coordinate system for the rigid-liquid-flexible coupled spacecraft

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图 2 轴对称贮箱示意图

Figure 2. Schematic diagram of an axisymmetric storage tank

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图 3 柔性板示意图

Figure 3. Schematic diagram of a flexible plate

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图 4 单元坐标系与节点号

Figure 4. The element coordinate system and node numbers

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图 5 航天器耦合动力学计算流程图

Figure 5. The spacecraft coupling dynamics calculating flowchart

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图 6 做定轴转动柔性板示意图

Figure 6. Schematic diagram of a flexible plate in fixed-axis rotation

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图 7 柔性板旋转角速度变化图

Figure 7. The time history of the flexible plate angular velocity

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图 8 板末端位移变形响应

Figure 8. Responses of displacement at the end of the plate

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图 9 液体激励时程图

Figure 9. The liquid excitation time history

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图 10 液体晃动力响应

Figure 10. Responses of liquid sloshing force

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图 11 外激励力矩示意图

Figure 11. Schematic diagram of the external excitation torque

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图 12 柔性板末端位移对比图

Figure 12. Comparison of displacements of the flexible plate

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图 13 航天器速度对比图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 13. Comparison of spacecraft velocities

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图 14 航天器角速度对比图

Figure 14. Comparison of spacecraft angular velocities

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图 15 十字形柔性板示意图

Figure 15. Schematic diagram of a cross-shaped flexible plate

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图 16 十字形柔性板网格划分图

Figure 16. The mesh division of a cross-shaped flexible plate

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图 17 微重力情况下航天器三轴速度响应

Figure 17. Triaxial velocity response of the spacecraft in microgravity

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图 18 微重力情况下航天器三轴角速度响应

Figure 18. Triaxial angular velocity responses of the spacecraft in microgravity

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图 19 柔性帆板末端位移对比图

Figure 19. Comparison of the displacements of the end of the flexible plate

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表 1 柔性板动力学模型仿真计算参数

Table 1. Simulating calculation parameters for the dynamic model of a flexible plate

parameter	value	parameter	value
elastic modulus/GPa	70	Poisson’s ratio	0.3
plate density/(kg·m^－3)	2 000	flexible plate rotation law around axis a₂	$ \dot{\omega}= \begin{cases}\frac{\varOmega}{T}\left(t-\frac{T}{2 \mathsf{π}} \sin \frac{2 \mathsf{π} t}{T}\right), & 0 \leqslant t \leqslant T, \\ \varOmega, & t>T\end{cases}$
plate length /m	1.828 8	total rotation time/s rotational angular velocity/(rad·s^-1)	30 0.2π
plate width/m	1.219 2	plate thickness /m	0.002 54

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表 2 液体晃动动力学模型仿真计算参数

Table 2. Simulating calculation parameters for the liquid sloshing dynamics model

parameter	value	parameter	value
liquid density/(kg·m^－3)	1 000	excitation amplitude/mm	3.04
tank diameter/m	0.148	excitation frequency/Hz	1.5
fill ratio	0.5	gravitational acceleration/(m·s^－2)	9.8
surface tension/(N/m)	0.072 5	excitation direction	X axis

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表 3 刚-液-柔耦合动力学模型仿真计算参数

Table 3. Simulating calculation parameters for the rigid-liquid-flexible coupling dynamics model

parameter	value	parameter	value
plate elastic modulus/GPa	4.45	liquid density/(kg·m^－3)	1 000
plate density/(kg·m^－3)	94.5	tank diameter/m	0.4
plate length/m	9	liquid fill ratio	0.4
plate width/m	3	surface tension/(N/m)	0.072 5
plate thickness/m	0.026 2	tank coordinate values in the spacecraft/m	(-0.1, -0.15, -0.4)
Poisson’s ratio of the plate	0.3	spacecraft quality/kg	5 000
plate coordinate values in the spacecraft/m	(1, 0, 0)	3-axis inertia moment of the spacecraft /(kg·m²)	(1 250, 1 250, 1 500)
		gravitational acceleration /(m·s^－2)	0.02

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表 4 充液航天器仿真计算参数

Table 4. Simulating calculation parameters for the liquid-filled spacecraft

parameter	value	parameter	value
plate elastic modulus/GPa	4.45	liquid density/(kg·m^－3)	1 000
plate density/(kg·m^－3)	94.5	tank diameter/m	0.8
single plate length/m	10	liquid fill ratio	0.4
single plate width/m	6	surface tension/(N/m)	0.072 5
plate thickness/m	0.026 2	tank coordinate values in the spacecraft/m	(-0.1, -0.15, -0.4)
1st order frequency of the plate/Hz	0.103 7	1st order frequency of liquid/Hz	0.104 3
2nd order frequency of the plate/Hz	0.777 9	2nd order frequency of liquid/Hz	0.179 6
3rd order frequency of the plate/Hz	2.222 7	3rd order frequency of liquid/Hz	0.181 5
Poisson’s ratio of the plate	0.3	spacecraft mass/kg	5 000
plate coordinate values in the spacecraft/m	(1, 0, 0)	3-axis inertia moment of a spacecraft/(kg·m²)	(1 250, 1 250, 1 500)
number of plates	6	gravitational acceleration /(m·s^－2)	0.02

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