Purpose <p>In order to meet the requirements of higher precision and broadband vibration reduction for aerospace components, it is urgent to design an efficient and stable Nonlinear Energy Sink (NES) to enhance its damping efficiency under low excitation amplitude. In this paper, negative stiffness and inerter element are introduced into the NES model to investigate its dynamic characteristics and vibration reduction effect.</p> Methods <p>Firstly, the slow-varying equation of the coupled system is obtained by means of the complex variable averaging method (CVAM). The effects of mass ratio, inerter-mass ratio and external excitation frequency on saddle-node bifurcation and Hopf bifurcation characteristics are further studied. Secondly, the excitation threshold of the system to generate the strongly modulated responses (SMR) is obtained based on the multi-scale method, and the fourth-order Runge-Kutta method is employed for numerical verification. Meanwhile, the excitation threshold of periodic vibration in the well and chaotic vibration between the wells is analyzed based on the Melnikov method.</p> Results <p>The saddle-node bifurcation diagram and Hopf bifurcation diagram show that the inerter-mass ratio and the excitation frequency near the main resonance have important effects on the bifurcation boundary. Vibration suppression performance near the main resonance can be improved by increasing the linear stiffness ratio (i.e., decreasing the negative stiffness ratio), cubic stiffness ratio, or inerter-mass ratio. However, exceeding a certain threshold will lead to abnormal peaks in the energy spectrum of the controlled system.</p> Conclusions <p>By means of the energy spectrum and time domain analysis, it is verified that the proposed NES with inerter and negative stiffness can suppress vibration more effectively than the existing three NESs, which can provide theoretical support for the design and application of high-performance NES.</p>