Analysis of vibrational resonance in a quintic oscillator

Abstract

We consider a damped quintic oscillator with double-well and triple-well potentials driven by both low-frequency force f cos ωt and high-frequency force g cos Ωt with Ω ≫ ω and analyze the occurrence of vibrational resonance. The response consists of a slow motion with frequency ω and a fast motion with frequency Ω. We obtain an approximate analytical expression for the response amplitude Q at the low-frequency ω. From the analytical expression of Q, we determine the values of ω and g (denoted as ωVR and gVR) at which vibrational resonance occurs. The theoretical predictions are found to be in good agreement with numerical results. We show that for fixed values of the parameters of the system, as ω varies, resonance occurs at most one value of ω. When the amplitude g is varied we found two and four resonances in the system with double-well and triple-well cases, respectively. We present examples of resonance (i) without cross-well motion and (ii) with cross-well orbit far before and far after it. ωVR depends on the damping strength d while gVR is independent of d. Moreover, the effect of d is found to decrease the response amplitude Q. © 2009 American Institute of Physics.