Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator

Abstract

Stability, saddle-node and period-doubling bifurcation conditions for the LR model motion in a horizontal impact oscillator are determined analytically and numerically. The regions for such conditions are developed in parameter space. The stability and bifurcation conditions for all the motions of this impact oscillator depend strongly on the initial impact phase instead of excitation frequency. The chaotic motion of the LR model induced by the period-doubling bifurcation are investigated numerically. The period doubling, periodic motions are illustrated through displacement responses and phase planes. The strange attractors of the chaotic motion induced by period doubling are presented by use of phase planes and the Poincare mapping sections. The analytical and numerical predictions for the stability and bifurcation of the LR motion do not agree well as the non-LR periodic motions coexist with the RL motion, which needs to be further investigated.