Forced vibration analysis of a multidegree impact vibrator

The dynamics of a multidegree impact vibrator subject to harmonic loading is investigated. The system is represented by a lumped mass model which hits and rebounds from a rigid wall during vibration. The periodic solution to the equations of motion with N forcing cycles and P impacts is formulated. The variational equations and the resulting transition matrix for investigating local stability of the periodic solutions are derived. A two-degree-of-freedom example is analysed, and a variety of motion types are found. Chaotic windows are present between regions of periodic response, and at these boundaries N-P motions are prevalent. Low velocity impacts are evident at exciting frequencies away from the natural frequencies. Two basins of attraction are computed, and the sensitivity to initial conditions is noted. The quality of the N-P motion is discussed from an engineering application perspective. (C) 1998 Academic Press Limited.