Bifurcations of a harmonically excited system impacting between two moving rigid bodies near a 1:4 strong resonance point

A harmonically excited system with rigid body impacts is considered. The periodic motions and Poincare mapping of the vibro-impact system are derived analytically. A center manifold theorem technique is applied to reduce the Poincare mapping to a two-dimensional one, and the normal form mapping associated with 1:4 strong resonance is obtained. Two-parameter bifurcations of the fixed points of 1:4 strong resonance in the vibro-impact system are analyzed. The simulation results illustrate some interesting dynamical features: in the vibro-impact system, there exist Neimark-Sacker bifurcations of periodic-impact motions and tangent and fold bifurcations of period-4 orbits near the bifurcation point of 1:4 strong resonance