Combination resonance in a multi-excited weakly nonlinear vibration absorber

It is established that oscillators with a weakly nonlinear spring, also resonates for excitations with a different frequency than its natural frequency. The studied type of resonance is called combination resonance, that occurs if the natural frequency approximately equals a sum of the excitation frequencies. This resonance can dissipate energy from several frequencies simultaneously. If a weakly nonlinear oscillator is used as an absorber on a main system, it can damps several vibration modes simultaneously. If combination resonance occurs in the absorber, it vibrates with the excited frequencies and its own natural frequency, which is higher as it is a sum of the excitation frequencies. This implies a potentially higher speed and dissipation. A tuning method is proposed to ensure this resonance in the weakly nonlinear absorbers. Additionally, a structural modification is added to the absorber, which increases the range of vibration energy of the main system that yields combination resonances. Simulations are performed that validate the theoretical analysis and tuning.