温致材料弹性模量变化的刚-柔-热耦合系统动力学

杨煜林; 田青龙; 蔡陈生; 唐育聪; 任建伟; 董杨; 高辉遥; 赵振宇; 卢天健

doi:10.21656/1000-0887.450255

温致材料弹性模量变化的刚-柔-热耦合系统动力学

doi: 10.21656/1000-0887.450255

杨煜林^{1, 2,},
田青龙³,
蔡陈生⁴,
唐育聪⁴,
任建伟^{1, 2},
董杨^{1, 2},
高辉遥^{1, 2},
赵振宇^{1, 2, ,},
卢天健^{1, 2}

1.
南京航空航天大学航空航天结构力学及控制全国重点实验室, 南京 210016
2.
南京航空航天大学多功能轻量化材料与结构工信部重点实验室, 南京 210016
3.
河海大学机电工程学院, 江苏常州 213002
4.
上海航天控制技术研究所, 上海 201109

（我刊编委卢天健来稿）

基金项目:

国家自然科学基金 11972185

国家自然科学基金 12002156

国家自然科学基金 12302047

详细信息

作者简介:
杨煜林(1999—)，男，硕士生(E-mail: ylyang@nuaa.edu.cn)

通讯作者:
赵振宇(1986—)，男，副研究员，博士(通讯作者. E-mail: zhenyu_zhao@nuaa.edu.cn)

中图分类号: O313.7
计量
- 文章访问数: 42
- HTML全文浏览量: 13
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2024-09-19
- 修回日期: 2024-10-24
- 刊出日期: 2025-09-01

Dynamics of Rigid-Flexible-Thermal Coupled System With Temperature-Dependent Material Elastic Modulus

YANG Yulin^{1, 2
,},
TIAN Qinglong³,
CAI Chensheng⁴,
TANG Yucong⁴,
REN Jianwei^{1, 2},
DONG Yang^{1, 2},
GAO Huiyao^{1, 2},
ZHAO Zhenyu^{1, 2
, ,},
LU Tianjian^{1, 2}

1.
State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China
2.
MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures(MLMS), Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China
3.
College of Mechanical and Electrical Engineering, Hohai University, Changzhou, Jiangsu 213002, P. R. China
4.
Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai 201109, P. R. China

Contributed by LU Tianjian, M.AMM Editorial Board

摘要

摘要:
航天器在太空执行任务期间会受到复杂空间热环境载荷影响，导致其柔性结构的温度场发生显著变化，温度变化会引发结构的热动力学耦合强非线性的动力学响应，严重时会导致航天器失效. 对于大尺寸、低刚度的柔性结构，其母材弹性模量的微小变化会引起系统较大的响应，故有必要分析材料弹性模量随温度变化对刚-柔-热耦合系统动力学的影响规律. 该文以绝对节点坐标法(absolute nodal coordinate formulation, ANCF)为基础，采用位置和梯度作为表征位移场及温度场的广义坐标，考虑温度对材料弹性模量的影响，提出了位移场和温度场统一形函数插值的等参单元. 之后，根据虚功原理推导出系统的动力学方程，根据热量守恒定律推导出系统的传热方程，并采用广义α方法同时求解了每一个时间步内的两个方程. 首先通过Boley简支梁验证了该文所提模型的有效性，然后分别建立了旋转柔性梁和中心刚体-夹层帆板航天器的刚-柔-热耦合系统动力学模型，针对不考虑温致材料弹性模量变化和考虑温致材料弹性模量变化的不同工况，进行动力学分析和比较. 结果表明，相较于热应力，热环境下材料弹性模量的降低对系统响应的影响更为显著：对于旋转柔性梁，当角速度ω₀为2 rad/s和10 rad/s时，柔性梁端部的最大变形量相比于刚-柔耦合工况分别增大了9.7%和4.5%；对于中心刚体-夹层帆板，当力矩M₀为200 N · m和2 000 N · m时，帆板检测点的最大变形量相比于刚-柔耦合工况分别增大了8.7%和7.1%. 温度导致材料弹性模量的变化对刚-柔-热耦合系统动力学响应产生的影响不容忽视，该文结果可为航天器的控制系统设计提供重要参考.
- 刚-柔-热耦合 /
- 绝对节点坐标法 /
- 温致材料弹性模量变化
Abstract:
During space missions, spacecrafts are subjected to complex thermal loads in the space environment, suffering significant temperature variations in their flexible structures. These temperature variations can induce strongly nonlinear thermo-dynamic coupling responses, which may, in severe cases, cause spacecraft failure. For large and low-stiffness flexible structures, even a slight change in the material elastic modulus can result in significant system responses. Therefore, it is essential to analyze the effects of temperature-dependent elastic moduli on the dynamics of rigid-flexible-thermal coupled systems. The absolute nodal coordinate formulation (ANCF) was applied, where both displacement and temperature fields are described with positions and gradients as generalized coordinates. The temperature-dependent material elastic modulus was considered, and an isoparametric element with unified shape function interpolation for both displacement and temperature fields was proposed. The system's dynamic equations were derived based on the principle of virtual work, and the heat transfer equations were derived from the law of energy conservation. The generalized-α method was used to simultaneously solve these 2 sets of equations at each time step. The validity of the proposed model was first verified with the Boley simply supported beam. Then, the rigid-flexible-thermal coupled dynamic models were established for a rotating flexible beam and a spacecraft with a central rigid body and laminate solar panels. Dynamic analyses and comparisons were conducted for cases with and without temperature-induced changes in the material elastic modulus. The results show that, during the heat transfer process, compared to the effects of thermal stress on the system responses, the decrease in the material elastic modulus under thermal environment has a more significant impact on the system response. For rotating flexible beams, Ewith angular velocity ω₀=2 rad/s and 10 rad/s, the maximum tip deformation increases by 9.7% and 4.5% respectively compared to that in the rigid flexible coupling case. For the central rigid body sandwich panel, with moment M₀=200 N · m and 2 000 N · m, the maximum deformation at the test point increases by 8.7% and 7.1% respectively compared to that in the rigid flexible coupling case. The effects of temperature induced changes in the material elastic modulus on the dynamic responses of rigid flexible thermal coupling systems cannot be ignored, and the work provides a reference for the design of spacecraft control systems.
- rigid-flexible-thermal coupling /
- absolute nodal coordinate formulation /
- temperature-induced change in material elastic modulus
edited-by

edited-by
注释:

1) （我刊编委卢天健来稿）

HTML全文

图 1 ANCF单元

Figure 1. The ANCF element

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图 2 ANCF热力耦合单元

Figure 2. The ANCF thermal coupling element

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图 3 算法求解流程

Figure 3. The overall flow-chart of the computation algorithm

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图 4 简支梁上表面受瞬时热流载荷

Figure 4. A simply supported beam under suddenly applied heat input

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图 5 简支梁中点无量纲挠度时程曲线

Figure 5. Dimensionless midpoint deflection time histories of the simply supported beam plotted

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图 6 旋转柔性梁示意图

Figure 6. Schematic of a rotating flexible beam

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图 7 弹性模量随温度变化曲线

Figure 7. The temperature dependent elastic modulus curve

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图 8 不同转速下柔性梁的端部温度

Figure 8. Tip temperature curves of the flexible beam under different rotational speeds

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图 9 柔性梁端部的横向变形

Figure 9. Tip deformation curves of the flexible beam

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图 10 中心刚体-夹层帆板卫星示意图

Figure 10. Schematic of the rigid body-laminated solar panel

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图 11 夹层帆板示意图

Figure 11. Schematic of the laminated solar panel

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图 12 上/下面板母材的温变弹性模量

Figure 12. The temperature dependent elastic modulus of the material made of upper and lower panels

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图 13 芯层温变纵向和横向弹性模量

Figure 13. Temperature variations of longitudinal and transverse elastic moduli of the core layer

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图 14 当M₀=2 000 N · m时，不同时刻下的考虑弹性模量随温度变化的帆板横向变形云图

Figure 14. For M₀=2 000 N · m, the transverse deformation contours of the solar panel the changing elastic modulus with the temperature at different moments

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图 15 不同力矩下，检测点的温度

Figure 15. Temperature curves at the test point under different torques

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图 16 检测点横向变形

Figure 16. Transverse deformations at the test point

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图 17 中心刚体旋转角度

Figure 17. Rigid body rotation angles

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表 1 简支梁材料参数

Table 1. Material parameters of the simply supported beam

parameter	symbol	value
density	ρ/(kg·m^-3)	2 810
Young’s modulus	E/GPa	71
specific heat	c/(J·kg^-1·K^-1)	920
thermal-conductivity coefficient	k/(W·m^-1·K^-1)	140
thermal expansion coefficient	α/K^-1	2.3E-5

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表 2 旋转柔性梁材料参数

Table 2. Material parameters of the rotating flexible beam

parameter	symbol	value
density	ρ/(kg·m^-3)	1 000
specific heat	c/(J·kg^-1·K^-1)	10
thermal conductivity coefficient	k/(W·m^-1·K^-1)	150
thermal expansion coefficient	α/K^-1	2E-5

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表 3 柔性梁端部的最大变形及增量

Table 3. Max deformations and increments of the flexible beam

ω₀/(rad/s)	model	max deformation/m	Δ/%
2	rigid-flexible	0.129 2	9.7
2	variable E	0.141 7	9.7
10	rigid-flexible	0.457 2	4.5
10	variable E	0.477 6	4.5

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表 4 帆板模型参数

Table 4. Material parameters of the solar panel

parameter	symbol	value
density1	ρ₁/(kg·m^-3)	1 800
density2	ρ₂/(kg·m^-3)	50
specific heat	c/(J·kg^-1·K^-1)	10
thermal conductivity coefficient	k/(W·m^-1·K^-1)	500
thermal expansion coefficient	α/K^-1	2E-6

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表 5 检测点最大变形量及振动频率

Table 5. Max deformations and vibration frequencies at the test point

M₀/(N·m)	model	test point max deformation/m	Δ/%	test point vibration frequency/Hz
200	rigid-flexible	0.014 9	8.7	1.6
200	variable E	0.016 2	8.7	1.48
2 000	rigid-flexible	0.148 1	7.1	1.6
2 000	variable E	0.158 6	7.1	1.54

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