对影响快链条运动状态的相关参数的研究

A RESEARCH ON THE RELEVANT PARAMETERS THAT AFFECT THE MOTION OF THE FAST CHAINS

关于绳子、锁链这样的一维柔性物体的力学问题拥有悠久的历史。这类问题的传统处理方式是通过微元法列出线性常微分方程求解,大多数复杂情况的求解都涉及数值模拟方法的介入。但是,对于一些有明显链节的链条,我们发现其力学特性已经无法支撑起连续性的假设,因此本文试图从物理模型本身出发,建立了由若干根与地面呈一定倾角的棍子交错排列连接而成离散模型,并利用此模型重点研究了奇特的快链条现象,探讨了快链条下落的运动状态和棍子与地面的夹角、棍子数目、棍子长度、快链条下落初始高度等因素的关系,并尝试将此模型推广到另外一些经典离散变质量系统,为相关工程理论的建立提出了一定的新思路。

Mechanical problems of one-dimensional flexible objects like ropes and chains have had a very long history. The traditional solution for such problems is to solve linear ordinary differential equation given by infinitesimal method. Moreover, most of the solutions for more complex situations even involve method like numerical simulation analysis. However, when it comes to chain composed of distinct units, we have found it hard for its mechanical properties to support continuity hypothesis anymore. Therefore, this paper manages to establish a discrete physical model started with model itself, which consist of numbers of unparalleled sticks interlaced with each other that have a certain angle to the ground, and studies the intriguing fast-chain phenomenon emphatically utilizing this model. We have also discussed relation between its state of motion and effect variables like angle to the ground, number of the sticks, length of the sticks and the initial falling height of fast-chain. Furthermore, we attempted to generalize this model to other classic discrete variable mass system, which can offer a brand new idea for establishments of relevant engineering theory.