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.