Dynamic analysis of a three-degree-of-freedom collision vibration system with clearances

The dynamic behaviors of a three-degree-of-freedom collision vibration system with clearances are investigated with both theoretical and numerical methods in this paper. The periodic solution of the system is obtained through the modal superposition method. The stability of the system is studied in two scenarios: one in which the system is subjected to unilateral collisions and the other in which it is subjected to bilateral collisions. In both cases, the unilateral grazing bifurcation and symmetric periodic motion of the system are examined through the construction of a discontinuity mapping and the utilization of the composite Poincaré mapping method, respectively. Finally, numerical simulations are conducted to validate the previous theoretical analysis.