The motion of slender rods in narrow tubes involves the coupling of axial movements and transverse vibrations, in which the transverse vibration exhibits high frequency and chaotic characteristics. These characteristics render the computational cost of the time integration to the motions of rods and tubes expensive. To solve this problem, this paper proposes a novel time-averaged method, which contains two innovations: 1) By time averaging the traditional dynamic equations, the time-averaged dynamic equations describing the rod-tube system are established based on the time-averaged concept used in turbulence problems; 2) Two time-averaged contact models are developed, by fitting the time-averaged sample set using the polishing function and the machine learning, respectively, to construct the relationship between the time-averaged contact gaps and the time-averaged contact forces. The time-averaged method can use a large time step, which is far larger than that required for the time integration of traditional methods, thus reducing the computational cost. Inclined and rolling experiments of the rod-tube system, as well as numerical experiments of the control rod drop in a nuclear reactor, are conducted to validate the accuracy of the time-averaged method. Comparative analyses are carried out between the time-averaged method and six continuous contact models, demonstrating the high computational efficiency of the proposed method. Moreover, the experimental results can provide benchmark data for algorithm verification for scholars studying dynamic contact algorithms.

中文翻译：

---

分析管内运动细长杆的时间平均方法


细长杆在窄管内的运动涉及轴向运动和横向振动的耦合，其中横向振动表现出高频和混沌特性。这些特性使得棒和管的运动的时间积分的计算成本非常昂贵。针对这一问题，本文提出了一种新的时间平均方法，该方法包含两个创新点：1）通过对传统动力学方程进行时间平均，建立了描述杆管系统的时间平均动力学方程。湍流问题中使用的概念； 2）通过分别使用抛光函数和机器学习拟合时间平均样本集，开发了两个时间平均接触模型，以构建时间平均接触间隙和时间平均接触力之间的关系。时间平均方法可以使用较大的时间步长，远大于传统方法时间积分所需的时间步长，从而降低了计算成本。进行了棒管系统的倾斜和滚动实验以及核反应堆控制棒落下的数值实验，以验证时间平均方法的准确性。对时间平均方法与六种连续接触模型进行了对比分析，证明了该方法的高计算效率。而且，实验结果可以为研究动态接触算法的学者提供算法验证的基准数据。