Galilean炮在刚性壁上的回弹1)

研究了Galilean炮——即若干个直径递增的弹性球组成的球链---撞击刚性壁回弹的问题。采用三种力学模型：分离刚体的多次"弹性"碰撞、多刚体的接触碰撞、以及有限元模拟，对球链撞击问题进行了分析，旨在给出碰撞结束后末端小球的飞离速度与入射速度的比值。研究表明：球链碰撞反弹后将会散开，末端小球的飞离速度明显大于球链入射速度；当入射球链间存在间隙时，末端小球的速度增幅更加明显。通过实验展现了这种末端小球回弹速度增加的现象。

REBOUNDING OF GALILEAN CANNON FROM A RIGID WALL1)

The Galilean Cannon involves a chain of different size balls rebounding on a rigid wall. Three mechanical models are used to analyze the rebound process: (1) The rebounding is treated as a series of separated one-to-one "elastic" impacts; (2) The rebounding is treated as a one-dimensional multi-body impact, using the Hertzian contact model to describe the rigid body interactions; and (3) The rebounding process is simulated using a 3-D FEM software. Each model reveals a disintegration phenomenon of the ball-chain after impact. It is shown that the rebound speed of the smallest ball in the far end of the chain can be several times larger than the incident speed. The increase of the rebounded speed is more significant when a spacing is assigned between the balls so that the multi-impacts occur as "separated" impact events. Also the differences among the three analytical models are discussed. Experiments are conducted with agreeable results as compared with the theoretical analysis.