Bursting oscillations in an isolation system with quasi-zero stiffness

•The bursting mechanism is revealed by bifurcation analysis of the system.•An approximation method for force transmissibility is proposed.•Bursting is generated from equilibrium to limit cycle and the equilibrium jumping.•The weakest bursting occurred when system behaves a unique equilibrium. In this paper, we investigate the bursting oscillations in a vibration isolation system with quasi-zero stiffness to improve the efficiency and reliability. The complex nonlinear dynamics are studied by the bifurcation analysis of both generalized autonomous system and non-autonomous system to reveal the mechanism and modes of bursting oscillations. An approximation method for force transmissibility is proposed by using peak intersection of bursting oscillations to show the impact of bursting on vibration isolation. The results obtained in this paper show that the bursting generations are caused by both the transition from equilibrium to limit cycle and the equilibrium jumping. The main outcome of this paper is that the weakest bursting occurred when the system behaves single equilibrium, which avoids the influence on isolation efficiency and improves the system reliability.