A theoretical model for a low-frequency two-stage hybrid vibration isolator with a nonlinear energy sink and a negative stiffness spring

Abstract

This paper proposes a new design philosophy of integrating a nonlinear energy sink (NES) with a negative stiffness spring (NSS) to construct a two-stage hybrid vibration isolator for low-frequency vibration attenuation. A theoretical model of the proposed two-stage hybrid vibration isolator is established to investigate the vibration isolation performance. The effect of a linear vibration absorber (LVA), the NES, and the NSS on the force transmissibility of the structure is compared, in which the parametric study including negative stiffness coefficient, mass ratio, frequency ratio, and barrier height is conducted. The nonlinear dynamic characteristics and energy transfer efficiency of the vibration isolation system are analyzed based on motion phase trajectories, Poincaré mapping and chaotic bifurcation analysis. The results demonstrate that the two-stage isolator with the NES and NSS architecture exhibits superior broadband vibration isolation compared to its counterpart with the LVA and NSS. The structure with the LVA and NSS shows a wider forbidden band range than the device without the LVA. Besides, the negative stiffness configuration between the vibration source and the protected base is a critical factor to influence vibration isolation. A larger negative stiffness coefficient results in lower force transmissibility and the onset frequency of the forbidden zone but the broader bandwidth of the forbidden zone. This work paves a new theoretical venue for low-frequency hybrid vibration isolators in precision instrument fields.