Quasiperiodic Route to Transient Chaos in Vibroimpact System

Abstract

Dynamic behaviour of the nonsmooth systems is interesting and explored subject in nonlinear science. We studied quasiperiodic route to chaos in nonlinear nonsmooth discontinuous vibroimpact system. In narrow frequency range different oscillatory regimes have succeeded each other many times under very small control parameter varying. There were periodic subharmonic regimes—chatters, quasiperiodic, and chaotic regimes. There were the zones of transition from one regime to another, the zones of prechaotic or postchaotic motion. The hysteresis effects (jump phenomena) occurred for increasing and decreasing frequencies. The chaoticity of obtained regime has been confirmed by typical views of Poincare map and Fourier spectrum, by the positive value of the largest Lyapunov exponent, and by the fractal structure of Poincare map. Discontinuous bifurcations are also described—it is phenomenon unique for nonsmooth systems. It is discussed the largest Lyapunov estimation for nonsmooth vibroimpact system.