Stability of periodic modes and bifurcation behaviors in a bouncing-dimer system

摘要: Recent experiments and simulations have shown that a dumbbell-shaped body, termed as dimer, on vibrating plate exhibits an amazing self-ordered phenomenon, in which its horizontal motion can take directed transport behavior when the body bounces periodically. While existing investigations detailed dynamics comprehensively, it still remains unclear how physical parameters of system affect emergence intriguing phenomenon. In this paper, we first reduce numerical model into simple under assumption one end always stays plate, while other The simplification modeling enables us to establish discrete map focusing impact bouncing end. Then, stability periodic be addressed by analyzing property around fixed points. Finally, properties behaviors quantified explicit relation between coefficient restitution e vibration intensity \(\varGamma \). developed theoretical results demonstrate rich nonlinear phenomena, including modes, chattering, multiperiodicity, period-doubling bifurcation, chaos. Guided predictions, performed via simulations. Comparison with obtained from reveals analytical are very effective accurate predictions.