Analytical solution to impact between a particle and an Euler-Bernoulli beam at arbitrary positon on the beam

The transverse impact between a particle and a simply supported beam is investigated. The direct mode superposition method (DMSM) is used to solve this initial value problem of the whole system. The impact point is located at arbitrary position on the beam. Supposing the deflection functions of the two parts of the beam separated by the impact point, the frequency equation of the whole system is established according to the initial condition, the continuity condition and the boundary condition. Then, using Duhamel integration the analytical solution is obtained to the beam impacted by the particle. With a numerical example, the convergence of the variables, such as, the impact force, deflection and moment is discussed. Curves of these variables varying with time are presented. The results show the effectiveness of the DMSM method.