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田青龙, 於祖庆, 兰朋, 陆念力. 热-动力学耦合多体系统建模与降阶. 力学学报, 2022, 54(9): 2588-2600. DOI: 10.6052/0459-1879-22-207
引用本文: 田青龙, 於祖庆, 兰朋, 陆念力. 热-动力学耦合多体系统建模与降阶. 力学学报, 2022, 54(9): 2588-2600. DOI: 10.6052/0459-1879-22-207
Tian Qinglong, Yu Zuqing, Lan Peng, Lu Nianli. Thermal-dynamic coupled analysis and model order reduction of multibody system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2588-2600. DOI: 10.6052/0459-1879-22-207
Citation: Tian Qinglong, Yu Zuqing, Lan Peng, Lu Nianli. Thermal-dynamic coupled analysis and model order reduction of multibody system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2588-2600. DOI: 10.6052/0459-1879-22-207

热-动力学耦合多体系统建模与降阶

THERMAL-DYNAMIC COUPLED ANALYSIS AND MODEL ORDER REDUCTION OF MULTIBODY SYSTEM

  • 摘要: 在轨运行的卫星天线受到太阳辐射热冲击后容易出现热致振动或指向不准确等问题, 严重时会导致航天器失效. 本文提出了一种基于改进模态综合法的刚柔热耦合多体系统建模与降阶方法. 采用绝对节点坐标法单元形函数对柔性天线的位移场与温度场进行统一离散插值, 避免了两种物理场网格不匹配带来的映射误差与效率问题, 并使用绝对节点坐标参考节点描述中心刚体. 在系统方程中考虑了热流输入和表面自热辐射. 针对绝对节点坐标法切线刚度阵高度非线性的特点, 利用一阶泰勒展开对系统动力学和传热学方程进行了分段线性化, 在线性化区间内切线刚度矩阵为常数矩阵, 避免了每个时间步上的弹性力及其雅克比矩阵的迭代计算, 并使得基于模态的降阶手段得以应用. 利用改进的模态综合方法划分子结构并缩减系统自由度. 相邻子结构之间通过约束方程保证连接精度和连续性. 通过纯导热半圆形薄板、薄板的热膨胀、柔性太阳能电池板和刚柔热耦合抛物线天线四个数值算例验证本文所提出方法的有效性. 结果表明, 本文提出的方法在保证仿真精度的前提下缩减了系统规模, 提高了仿真计算效率.

     

    Abstract: Under the impacted of solar heat flux, the satellite antenna in orbit is prone to thermally induced vibration or inaccurate pointing, which will lead to spacecraft failure in serious cases. In this study, a modeling and model order reduction method for rigid flexible thermal coupling multibody system based on the improved component mode synthesis method is proposed. First of all, the displacement and temperature field of the flexible antenna are discretized by the unified element shape function of the absolute node coordinate formulation (ANCF), which can avoid the mapping error and efficiency problems caused by the mismatching of the two physical fields. The ANCF reference node is used to describe the central rigid bodies. In addition, the solar heat flux input and the surface emitting radiation are considered in the system equation. According to the highly nonlinear characteristics of the tangent stiffness matrix of the ANCF, the first-order Taylor expansion is used to linearize the dynamic and heat transfer equations. The tangent stiffness matrix in the linearized horizon is a constant matrix, which avoids the iteration of the elastic force and its Jacobian matrix in each time step, and makes the model order reduction method could be applied. Afterwards, the improved component mode synthesis method is used to divide the substructure and reduce the degrees of freedom of the system. The substructures are connected by constraint equations to ensure the accuracy and continuity between the structures. At last, four numerical examples such as the pure heat conducting semicircular thin plate, the thermal expansion of thin plate, the flexible solar panel and the rigid flexible thermal coupling parabolic antenna are given to verify the effectiveness of the proposed method. The results show that the proposed method can reduce the scale of the system and improve the efficiency of simulation calculation without losing accuracy.

     

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