论文标题
振动对恢复系数的影响
Vibrational Effects on the Coefficient of Restitution
论文作者
论文摘要
一个球从给定的高度掉落到表面上，将反复反弹，然后再休息。在厚板上弹跳的球的行为与从容器的薄盖上弹跳的球的行为会大不相同。对于具有固定厚度的板，在板边缘弹跳的球将与球从板的中间弹跳在一起。我们研究了具有各种厚度的钢球弹跳钢板的恢复原状$ε$。我们观察到$ε$随着球重复弹跳而终于休息时会发生变化。通常，由于球的动能耗散到板上，$ε<1 $。但是，这种消散的能量可以在后来的弹跳中恢复到球中。我们看到超弹性碰撞的出现（$ε> 1 $），这意味着球由于与板的碰撞而获得了动能。我们可以通过在球中添加弹簧来增加这种超弹性碰撞（p $ _ {se} $）的可能性。我们构建了一个简单的理论模型，在该模型中，以前的碰撞中损失的能量被转移到后来的碰撞中。该模型能够模拟这种超弹性碰撞的发生。
A ball dropped from a given height onto a surface, will bounce repeatedly before coming to rest. A ball bouncing on a thick plate will behave very differently than a ball bouncing off the thin lid of a container. For a plate with a fixed thickness, a ball bouncing at the edge of a plate will be very different from the ball bouncing off the middle of the plate. We study the coefficient of restitution $ε$ for a steel ball bouncing steel plates of various thicknesses. We observe how $ε$ changes as the ball repeated bounces and finally comes to rest. Generally, $ε< 1$ due to the dissipation of kinetic energy of the ball into the plate. However this dissipated energy can come back into ball in its later bounces. We see the emergence of super-elastic collisions ($ε> 1$), implying that the ball gained Kinetic Energy due to the collision with the plate. We can increase the probability of such super-elastic collisions (P$_{SE}$) by adding a spring to the ball. We construct a simple theoretical model where the energy lost from previous collisions are transferred back into later ones. This model is able to simulate the occurrence of such super-elastic collisions.
