Effective-parametric resonance in a non-oscillating system

Abstract

We present a mechanism for the generation of oscillations and nonlinear parametric amplification in a non-oscillating system, which we term effective-parametric resonance. Sustained oscillations appear at a controlled amplitude and frequency, related directly to the external forcing parameters. We present an intuitive explanation for this phenomenon, based on an effective equation for a driven oscillation and discuss its relation to other approaches. More precisely, a high-frequency forcing can generate an effective oscillator, which may have a parametric resonance with the applied forcing. We point out the main ingredients for the development of effective-parametric resonance in non-oscillating systems and show its existence in a simple model. Theoretically, we calculate the appearance of this nonlinear oscillation by computing its stability curve, which is confirmed by numerical simulations and experimental studies on a vertically driven pendulum.