无动力运动球体在沙地上的运动探究

Research on the motion of an unpowered moving sphere on the sand

本文基于阻力模型,在引入惯性阻力、粘滞阻力和根据阿基米德修正定律得到的静态阻力基础上对在颗粒介质上具有初速度的无动力小球运动这一经典穿透动力学问题进行分析.通过小球运动的动力学方程,得到了其在颗粒介质上的最长滑行距离的定量解,还探究了颗粒密度,颗粒堆积密度、颗粒半径,颗粒介质安息角、小球半径、小球密度,颗粒介质杨氏模量,及初速度对小球运动距离的影响.并发现阻力模型理论与实验有较好的吻合度.

Based on the resistance model,this paper analyzes the classical penetration dynamics problem of an unpowered ball motion with initial velocity on a granular medium by introducing inertial resistance,viscous resistance and static resistance derived from Archimedes modified law.A quantitative solution of the longest sliding distance of the pellet on the particle medium is obtained by means of the kinetic equation of the pellet motion.The particle densityρ_0,particle packing densityρs,particle radius r,sphere radius R,sphere densityρb,Young s modulus G of the particle medium are also investigated.And the influence of initial velocity v 0 on the distance of small ball.It is found that the theory of resistance model is in good agreement with the experiment.