Purpose <p>Nonlinear energy sink (NES) is a kind of energy absorber that has special importance in reducing structural vibration. The existing research results on NES indicate that the study of the vibration characteristics of the system induced by frequency detuning is not sufficiently comprehensive. Furthermore, the vibration characteristics of multi-degree-of-freedom NES have received relatively limited research attention. This research investigates the vibration characteristics of the system with a new 2-dof NES considering the influence of frequency detuning.</p> Methods <p>Firstly, the Cardano discriminant, the incremental harmonic balance method, and Floquet theory are employed to investigate the bifurcation behavior of the 3-dof system with and without frequency detuning. Secondly, the strongly modulated response (SMR) of the 3-dof system is analyzed through numerical simulations. Lastly, energy spectra are used to evaluate the vibration suppression performance of the proposed 2-dof NES.</p> Results <p>This study shows that the response amplitude of the 3-dof system decreases as the mass of the 2-dof NES increases. Meanwhile, it can be observed that the system with 2-dof NES exhibits SMR when the system with 1-dof NES shows either steady-state responses or weak modulation responses. Furthermore, the system with 2-dof NES has a smaller energy area than the system with 1-dof NES under the same parameters.</p> Conclusion <p>The results demonstrate that a properly designed 2-dof NES exhibits superior vibration suppression compared to a 1-dof NES under the same parameters.</p>