利用DMSM方法求解弹性撞击恢复系数

SOLUTION OF THE COEFFICIENT OF RESTITUTION FOR ELASTIC IMPACT USING DMSM

给出了物体与细长杆或梁弹性碰撞恢复系数的一种求解方法。在研究碰撞问题时,把碰撞物作为靶体的附加质量,从而把碰撞问题转化为常规的振动问题求解.两个撞击物的分离时刻根据撞击力为零得到.结论如下:只考虑弹性碰撞时,恢复系数不仅与靶体的材料性质有关,还与碰撞物体质量比、靶体的支承条件有关,但与碰撞的初始速度无关.

An analytical solution for the coefficient of restitution of a mass colliding with a slender rod or beam was presented. The colliding body was regarded as the attachment of the target, so the problem was transformed into a normal vibration problem using DMSM （Direct Mode Superposition Method）. The separation moment was obtained by setting the impact force as zero. It can be concluded that, when only elastic impact is considered, the coefficient of restitution is determined by not only the material property of the target, but also the mass ratio of the colliding body to the target, and the boundary condition of the target. However, the initial velocity has no effect on the coefficient of restitution.