VIBRATION ABSORBERS FOR A CLASS OF SELF-EXCITED MECHANICAL SYSTEMS

An averaging methodology is employed in studying dynamics of a two-deg ree-of-freedom nonlinear oscillator. The main system is modeled as a v an der Pol oscillator under harmonic forcing. The objective is to redu ce its amplitude of oscillation near resonance, by attaching to it a d amped vibration absorber with a Duffing spring. It is first shown that substantial reduction in the response amplitude can be achieved in th is way. Ho wever, for some combinations of the parameters, the low-amp litude periodic motion of the system in the original resonance regime becomes unstable through a Hopf bifurcation of the averaged equations. Direct numerical integration shows that this gives rise to amplitude modulated or chaotic response of the oscillator, with much higher vibr ation amplitudes than the unstable periodic response, which coexists w ith these complex motions. Finally, it is shown that the present analy sis can be employed in selecting the parameters in ways that exploit t he significant practical advantages arising from the presence of the a bsorber, by predicting and avoiding these instabilities.