Stabilization of 1/3-Order Subharmonic Resonance Using an Autoparametric Vibration Absorber

Abstract

The paper proposes a stabilization method for 1/3-Order subharmonic resonance with an autoparametric vibration absorber. A main system with nonlinear spring stiffness and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces 1/3-Order subharmonic resonance. A damped pendulum system, whose natural frequency is in the neighborhood of one-half of the main system, is attached to the main system as an absorber, in order to induce 1:2 internal resonance. The 1/3-Order subharmonic resonance which occurs in the case of locked pendulum is avoided due to energy transfer between the main system and the absorber, and due to energy dissipation by the absorber. It is also theoretically shown that a stable nontrivial steady state with respect to the 1/3-Order subharmonic frequency component is changed into an unstable one due to the absorber. Experimental results show the validity of the autoparametric vibration absorber for the 1/3-Order subharmonic resonance.