PERIODIC AND CHAOTIC BEHAVIOR OF A THRESHOLD-LIMITED 2-DEGREE-OF-FREEDOM SYSTEM

A two-degree-of-freedom impact oscillator with proportional damping is considered. The maximum displacement of one of the masses is limited to a threshold value by a rigid wall, which gives rise to a non-linearity in the system. Impacts between the mass and the wall are described by a coefficient of restitution. The behaviour of the system is rich and includes features like period doublings, period halvings, jumps, chaos, etc. Periodic motions of the system are studied by analytical methods. The influence of system parameters such as damping, coefficient of restitution, distribution of masses and clearance, etc., is studied for some extreme values of these parameters. The stability of a class of periodic motions is investigated. Parameter ranges which result in stable periodic multiple impacts are identified. Application of the results to the design of impact tools is discussed. © 1993 Academic Press. All rights reserved.