Frequency-comb response of a parametrically-driven Duffing oscillator to a small added ac excitation

TL;DR

This paper models a nonlinear parametrically-driven resonator that produces a frequency comb-like spectrum with narrow peaks, and demonstrates how a small added ac signal influences its stability and spectral response.

Contribution

It introduces a one-degree-of-freedom nonlinear model showing frequency comb responses and analyzes the effects of an added ac signal on parametric instability.

Findings

Spectral responses resemble a frequency comb with equally spaced peaks.

Added ac signal can suppress parametric instability.

Averaging method effectively captures the system dynamics.

Abstract

Here we present a one-degree-of-freedom model of a nonlinear parametrically-driven resonator in the presence of a small added ac signal that has spectral responses similar to a frequency comb. The proposed nonlinear resonator has a spread spectrum response with a series of narrow peaks that are equally spaced in frequency. The system displays this behavior most strongly after a symmetry-breaking bifurcation at the onset of parametric instability. We further show that the added ac signal can suppress the transition to parametric instability in the nonlinear oscillator. We also show that the averaging method is able to capture the essential dynamics involved.