Abstract: Vibratory systems with repeated impacts are considered. Dynamics of such systems, in inelastic impact cases, are studied with special attention to existence of two different types of periodic-impact motions, bifurcations and singularity by applying bifurcation theory of mapping. Regularity and transition of two types of periodic-impact motions are studied by use of a mapping derived from the equations of motion. The mapping of vibratory systems with repeated inelastic impacts is of piecewise property due to synchronous and non-synchronous motions of impact components immediately after the impact, and singularities caused by the grazing contact motions of impact components. The piecewise property and grazing singularity of Poincaré mapping of such systems lead to non-standard bifurcations of periodic-impact motions. The influence of the piecewise property and singularities on global bifurcations and transitions to chaos is elucidated. The routes from periodic-impact motions to chaos are analyzed by numerical analyses.

Key words: Grazing bifurcation, Impact, Periodic motion, Sliding bifurcation, Vibration