In the present study, the focus is set on the development of a design methodology for nonlinear vibration absorbers, termed nonlinear energy sink (NES), to optimize the vibrating level reduction on a Duffing oscillator. The idea lies in the assessment of a duality property between, on the one hand, the tuning procedure of the tuned mass damper (TMD) coupled to a linear oscillator and, on the other hand, the assumed design scheme of NES coupled to a purely nonlinear Duffing oscillator. To this end, the basics on the TMD tuning methodology are recalled and extended to the concept of frequency-energy plot (FEP) [1]. Then, based upon this concept, the development of a NES design procedure is undertaken and the related dynamics analyzed. Finally, it is shown how to design a vibration absorber to deal with a general Duffing oscillator.
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