Dynamic modulation induced by constraint stiffness in a periodically forced vibration system

A dual-mass collision system with elastic constraints is established. The nonlinear dynamic equations governing the system are derived, from which a Poincaré map is constructed to analyze its intermittent contact dynamics. A multi-dimensional coupling analysis is conducted to investigate the influence of constraint stiffness on system dynamics. Two-dimensional parameter-variable bifurcation diagrams reveal the governing mechanisms of stiffness thresholds on motion diversity. Single-variable bifurcation diagrams elucidate the evolution of periodic orbits, while phase trajectory diagrams combined with Lyapunov exponents clarify the dynamic origins of subharmonic multi-impact motions in high-frequency range. The research findings demonstrate that constraint stiffness exhibits a proportional relationship with the quantity of one-period multi-impact motion clusters. The intrinsic mechanism of subharmonic motions in high-frequency range is attributed to the dynamic coupling interaction between one-period single-impact and n-period single-impact motions. The irreversible nature of transitions between adjacent one-period multi-impact responses is investigated, accompanied by the identification of two transition regions: hysteresis and tongue-shaped domains. The mechanism and evolution of subharmonic motions in tongue-shaped domains are systematically analyzed. Cell mapping is applied to identify the basin distribution of coexisting attractors. Investigations on other system parameters establish a theoretical foundation for enhancing motion stability control in mechanical systems with clearance.