Vibrations of nonlinear systems with discontinuities - (The case of a preloaded compliance system)

This paper deals with vibrations of a preloaded compliance system as an exa mple of vibrations of nonlinear systems with discontinuities. The resonance curves of harmonic, higher harmonic and subharmonic vibrations are obtaine d by using the direct numerical integral method presented previously, which is a highly accurate shooting method. Chaos is generated in the system tre ated here, Influences of amplitude and frequency of external force and damp ing ratio on the resonance curves and the stability of solutions are discus sed. It is found that ii a trajectory enters a discontinuous point, a bifur cation is realized. A stable periodic solution becomes unstable due to this bifurcation and chaos may suddenly occur at the halfway point of the perio d-doubling route. This route to chaos is same as the one found in the force d self-excited vibration system with dry friction.