Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.