Bifurcation Sequences of Vibro-Impact Mechanical Systems in 1:4 Resonance Case

A forced oscillator with a free rigid body, is considered. Local dynamical behavior of the impact oscillator, under 1:4 strong resonance condition, is studied. Some interesting dynamical features near 1:4 resonance point are found for the impact oscillator, including Neimark-Sacker bifurcation of single-impact periodic motion, tangent and fold bifurcations of period-4 four impact motion, etc. Quasi-periodic impact orbit, associated with period-1 motion, is created through Neimark-Sacker bifurcation, but destroyed as a tangent bifurcation of period-4 four-impact motion occurs.