The coexisting periodic impacting motions and their multiplicity ofa kind of dual component systems under harmonic excitation are analytically derived.The stability condition of a periodic impacting motion is given by analyzing the prop-agation of small, arbitrary perturbation from that motion. In numerical simulations,the periodic impacting motions are classified according to the system states beforeand after an impact. The numerical results show that there exist many types ofvibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.
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