Vibrations of Nonlinear Systems with Discontinuities : The Cace of a Preloaded Compliance System

This paper deals with vibrations of a preloaded compliance system as an example of vibrations of nonlinear systems with discontinuities. The resonance curves of harmonic, higher-harmonic and subharmonic vibrations are obtained by using the direct numerical integral method presented previously, which is a highly accurate type of shooting method. Chaos is generated in the system treated here. Influences of amplitude and frequency of an external force and damping ratio on the resonance curves and the stability of solutions are discussed. It is found that if a trajectory enters a discontinuous point, a bifurcation is realized. A stable periodic solution becomes unstable by this bifurcation and chaos may suddenly occur at the halfway point of the period doubling route. In this way, another chaos route was also found in a preloaded compliance system in the same manner as in the forced self-excited vibration system with dry friction.