Bifurcation analysis of a piecewise-linear impact oscillator with drift

摘要: We investigate the complex bifurcation scenarios occurring in dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively behaviour drilling systems. This system has been extensively studied by numerical and analytical methods past, but its intricate structure largely remained unknown. For analysis, we use computational package TC-HAT, toolbox AUTO 97 for continuation detection periodic orbits non-smooth dynamical systems (Thota Dankowicz, SIAM J Appl Dyn Syst 7(4):1283–322, 2008) The study reveals presence co-dimension-1 -2 bifurcations, including fold, period-doubling, grazing, flip-grazing, fold-grazing double grazing bifurcations limit cycles, as well hysteretic effects chaotic behaviour. Special attention given rate how it affected control parameters.