The paper deal with the passive control of resonant systems using nonlinear energy sink (NES). The objective is to highlight the benefits of adding nonlinear geometrical damping in addition to the cubic stiffness nonlinearity. The behavior of the system is investigated theoretically by using the mixed harmonic balance multiple scales method. Based on the obtained slow flow equations, a design procedure that maximize the dynamic range of the NES is presented. Singularity theory is used to express conditions for the birth of detached resonance cure independently of the forcing frequency. It is shown that the presence of a detached resonance curve is not necessarily detrimental to the performance of the NES. Moreover, the detached resonce curve can be completely suppressed by adding nonlinear damping. The results of the design procedure are the compared to numerical simulations.