Dynamics of a two-degree-of freedom periodically-forced system with a rigid stop: Diversity and evolution of periodic-impact motions

• Dynamics is studied by multi-parameter and multi-performance co-simulation analyses.
• The generation mechanism of complete and incomplete chattering-impact motions is studied.
• The transition irreversibility of adjacent fundamental impact motions creates singular points.
• Abnormal and regular subharmonic impact motions dominate in the tongue-shaped region.
• Diversity and complexity of periodic-impact motions are found by multi-parameter analyses.

A two-degree-of-freedom periodically-forced system with a clearance is considered. The correlation between dynamic performance and system parameters is studied to find their feasible matching law. The fundamental group of impact motions is defined, which have the excitation period and differ by the number p of impacts. The generation mechanism of complete and incomplete chattering-impact vibration of the system is studied. A series of singular points between any two adjacent fundamental impact motions are found, at which real-grazing and bare-grazing bifurcation boundaries of one of them, saddle-node and period-doubling bifurcation boundaries of the other alternately intersect and create two types of transition regions: hysteresis and tongue-shaped regions. Subharmonic impact motions are found to regularly appear in the tongue-shaped regions. Based on the sampling ranges of parameters, dynamics of the system is studied with emphasis on the influence of system parameters on impact velocities, existence regions and correlative distribution of single-impact periodic motions by multi-parameter and multi-performance co-simulation analysis.