Two approximate methods of prediction of impact force of a small sphere on Euler-Bernoulli beam using restitution coefficient

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 governing 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.