2007 Volume 1 Issue 1 Pages 39-50
This paper deals with a two-degree-of-freedom forced system composed of a main system and an impact damper which has been analyzed by many researchers. Periodic solutions, bifurcations, chaos, and vibration quenching are discussed. A shooting method for impact systems presented by authors is used in numerical calculations. The following results were obtained: (1) Unsynmetric periodic solution with four collisions per period and subharmonic vibrations with many collisions were found. (2) Discontinuities in the stability of the periodic solutions caused by impact were shown using characteristic multipliers. (3) Two routes to chaos were found, namely, the period doubling route and the torus doubling route. (4) Hyper chaos was found for the first time in the impact damper system. (5) The vibration quenching problems for the narrow frequency region near the resonance point and for the wide frequency region were discussed.
