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The paper deals with the passive control of resonant systems using nonlinearenergy sink (NES). The objective is to highlight the benefits of addingnonlinear geometrical damping in addition to the cubic stiffness nonlinearity.The behaviour of the system is investigated theoretically by using the mixedharmonic balance multiple scales method. Based on the obtained slow flowequations, a design procedure that maximizes the dynamic range of the NES ispresented. Singularity theory is used to express conditions for the birth ofdetached resonance cure independently of the forcing frequency. It is shownthat the presence of a detached resonance curve is not necessarily detrimentalto the performance of the NES. Moreover, the detached resonance curve can becompletely suppressed by adding nonlinear damping. The results of the designprocedure are then compared to numerical simulations.

Increasing dynamic range of NESs by using geometric nonlinear damping