Experimental and theoretical analysis of the elastic-plastic normal repeated impacts of a sphere on a beam

The normal repeated impact of a sphere upon an elastic-plastic beam has been analyzed experimentally and theoretically. Hertz elastic contact model and seven well known elastic-plastic contact models were selected for theoretical analysis. A piecewise linearized method has been presented to linearize the nonlinear contact stiffness of eight selected contact models. Generalized closed-form solutions (theoretical solutions) of repeated impact response were derived for each piecewise linearization by vibration theory. Ahead of the theoretical study, to gain a deep insight into the eight selected contact models, an idealized repeated impact problem of elastic-plastic half space/foundation was solved by Runge-Kutta integration method. The numerical results show that the models are of large differences in predicting contact behavior, and reveal a strong correlation of the models with the two model parameters: the indentation of initial contact yield and the effective radius of contact curvature of unloading. Experiments were performed with regard to a repeated impact process of a sphere striking repeatedly at the center of the beam. The theoretical and experimental results show that selecting the appropriate contact model is very important on predicting contact behavior. No significant advantage of indentation type has been found over flattening type among these contact models. The divergences of contact behavior and the strong correlation for the eight contact models still exist. Compared with the experimental results, for the coefficient of restitution and the rebound velocity of the sphere, all of the eight contact models predict larger values and contrary trends on impact velocity compared to the experimental results. The reasons may come from wave effects and sub-impact phenomenon.