Control of Resonance by Chaos-Elucidation of Fundamental Mechanism

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To investigate whether the resonance due to external periodic forcing at a particular frequency can be suppressed or not by using chaotic oscillator is the purpose of this research and fundamental mechanisms are examined based on simple nonlinear oscillator models.In the usual dynamical vibration absorber, resonance is avoided by a shift of resonance frequency due to a subsidary oscillator attached to the main oscillator. On the contrary, the inserted oscillator model, i.e., a subsidary nonlinear oscillator is inserted in between the main system and the external periodic force, is theoretically examined with an expectation that if the external periodic force is changed to chaotic oscillations with broad band spectra, reductions of the resonant amplitude at a particular frequency might take place. It was observed numerically that broadening of energy due to chaos can actually suppress the resonance.Two types of inserted nonlinear oscillator models(i.e., uncoupled and coupled cases)are solved numerically under various conditions and resonant amplitudes as well as spectra of oscillations are examined in details. Results are summarized as follows :1. Nonlinear saturations due to the inserted nonlinear oscillator reduce significantly the resonant amplitudes of the main oscillator for both uncoupled and coupled cases.2. Further reductions of the resonant amplitudes are observed when the nonlinar inserted oscillator changes the external periodic force to oscillations with harmonics, sub-harmonics, or broad spectra as chaos.3. The differences between the dynamical vibration absorber and the inserted nonlinear oscillator model exhibit that the latter gives large shift of resonance frequency for weakly nonlinear case and nonlinear saturation effectively suppress resonance for strongly nonlinear case.Thus it is shown at least theoretically that the inserted nonlinear oscillator can work as an effective attenuator of resonance.