Dynamic behavior of circular ring impinging on ideal elastic wall: Analytical model and experimental validation

The transient dynamic behavior of an elastic thin-walled circular ring with low velocity impinging on an ideal elastic wall is investigated through analytical approach, numerical simulation and experimental observation. The motion of circular ring is approximated by the rigid-body displacement and those due to a few low-order modal vibrations, while the governing equations for the constrained motion stage and free motion stage are derived by employing the Lagrange procedure. The whole collision and rebounding process is then evaluated by solving the governing equations of two motion stages alternately. Analytical results illustrate that the coefficient of restitution, number of collisions and non-dimensional rebounding time are all dependent on the stiffness ratio of the elastic wall to the circular ring, the non-dimensional initial velocity and the ratio of the ring thickness to average radius. Numerical simulations and experimental tests were carried out to validate the applicability and accuracy of the analytical approach, and the multiple collisions phenomenon between the circular ring and elastic wall for large stiffness ratio is validated. This work reveals the remarkable influence of elastic vibration on the collision and rebounding behaviors of elastic components and could guide the selection of materials and stiffness in crashworthiness design.