Abstract
This study presents an analysis of the transient response of a beam subjected to transverse impact by a spherical particle. The beam is modeled as a long Timoshenko beam with clamped boundaries. A numerically stable solution to the dispersion relation is developed, which allows the deflection to include the effects of high-frequency waves. Time history of contact force, transverse deflection, velocity and acceleration provide insight into the interactions between the two objects after impact. Comparison with the Euler-Bernoulli beam model demonstrates the advantage of the Timoshenko beam in capturing the dispersive features of wave propagation. The group and phase velocities of bending waves due to impact are presented and show a good correlation with the time-domain analysis. The dependence of the coefficient of restitution on the mass ratio of the particle and the beam is discussed. Results show that the mass ratio divides the contact behavior of the particle and beam to a single-contact regime and multiple-contact regime and influences the coefficient of restitution (COR) value in different ways.
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