Control of primary and subharmonic resonances of a Duffing oscillator via non-linear energy sink

•Duffing oscillator endowed with a non-linear energy sink (NES) to passively control vibrations.•External 1:1 and 1:3 resonant harmonic excitations.•Application of a specific perturbation method to obtain amplitude modulation equations.•Verification of the beneficial effect of the NES in controlling primary and subharmonic resonances.•Good agreement between results provided by the perturbation method and the numerical integration of the original equations.

The use of non-linear energy sink to passively control vibrations of a non-linear main structure under the effect of bi-frequency harmonic excitation is addressed here. The excitation is assumed to induce both 1:1 and 1:3 resonance, and the response of the system is studied after using the Multiple Scale/Harmonic Balance Method, applied to obtain amplitude modulation equations in the slow time scale. The efficiency of the non-linear energy sink to reduce or suppress vibrations of the main structure is finally discussed.