Abstract
This paper deal with two-degree-of-freedom forced system composed of main system and an impact damper which has been analysed by many researchers. Periodic solutions, bifurcations, chaos, and the vibration control are discussed. A shooting method for impact systems presented by authers before are used in numerical calculation. As a result, the followings were made clear. (1) Unsynmetric periodic solution with 4 collisions per period and many subharmonic vibrations with many collisions were found. (2) The discontinuities in the stability of the periodic solutions caused by impact were shown using characteristic multiplier. (3) There were two routes to chaos, namely, period doubling route and torus doubling route were found. (4) Hyper chaos was found for the first time in the impacting system. (5) The design using synmetric periodic solutions with two collisions per period is not enough in the design of the impact damper.
