Periodic-impact motions and bifurcations of a dual component system

A two-degree-of-freedom vibratory system with a clearance and repeated impacts is considered. Dynamics of the system, in a perfectly plastic impact case, is studied by using a three-dimensional map. The map is of piecewise property due to synchronous and non-synchronous motion of two masses immediately after the impact, and singularities caused by the grazing contact motions of two masses. The influence of the piecewise property and singularities on global bifurcations and transitions to chaos is elucidated by analytical and numerical analyses. The vibratory system with a clearance and repeated impacts exhibits two different types of period nn single-impact motions in different forcing frequency regions, respectively. The results from the simulation show that period-doubling bifurcations of period nn single-impact orbits of the system are commonly existent. However, no period-doubling cascade occurs due to the piecewise and discontinuous nature of the map. Bifurcations of the plastic impact map are qualitatively very much different from those of usual consecutive maps. Synchronous motion of two masses, immediately after the impact, changes the two-degree-of-freedom vibro-impact system to a single-degree-of-freedom oscillator, which complicates the dynamic behavior of the repeated impact system considerably. Synchronous motion and grazing contact of two masses jointly lead unusual and complex sequences of transitions to chaos. The transitions, in the system with repeated plastic impacts, are more complicated than those in elastic impact oscillators.