利用恢复系数预报梁结构弹性正碰载荷的两种有效近似法

Two Approximate Methods of Prediction of Impact Force of a Small Sphere on Euler-Bernoulli Beam Using Restitution Coefficient

对于小球撞击欧拉—贝努利梁问题,应用撞击力模型,给出预报撞击力的两种方法。方法1基于位移协调方程,分别考虑碰撞发生阶段结束和恢复阶段结束两个时刻的位移协调方程。方法2基于梁的动力微分方程,利用撞击系统的动量守恒原理和恢复系数概念。两种方法均得到撞击过程中撞击力随时间变化的曲线。分析结果与已有结果进行比较,结果符合较好。其中方法1大幅简化计算量,可推广到小球与板撞击问题中去；方法2能够较好地描述撞击力,同时可分析各种因素对接触撞击力的影响。

For the problem of a small sphere impact on a Euler-Bernoulli beam using the impact model, two methods are presented for the prediction of the impact force. The first method is based on the displacement conformation equation. Two moments including the beginning moment in the impact initialization phase and the ending moment in the impact recovering phase are considered. The second method is based on the beam＇s gow erning motion equation, the momentum conservation law and the definition of the restitution coefficient. The curves of impact force with respect to time are obtained by the two methods. The results are compared with the previous known results. In Method 1, the amount of calculation is reduced largely, and the method can be extended to the problem of plate impact. Method 2 can be used to simulate the impact procedure well, and various factors influencing the impact force are analyzed.