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

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.

Stochastic resonance and amplification in the ac driven Duffing oscillator with added noise

“…Particularly relevant systems to be investigated for the effect of added noise are nonlinear resonators that can present frequency-comb spectra [22,23,25]. We believe that the method we developed here may help evaluate the robustness of mechanical frequency-comb generation in the presence of noise.…”

“…Furthermore, we develop equations to predict the effect of white noise on the pump, signal, and idler responses in a Duffing amplifier. This approach may prove to be useful for assessing the effect of added noise on the generation of frequency-comb spectra in mechanical resonators [21][22][23][24][25]. We also calculate the power spectral density of the response of the driven Duffing oscillator.…”

The effects of nonlinear damping on degenerate parametric amplification

“…Recent theoretical analysis for PA include the effects of quadratic and cubic nonlinearities [7], dual frequency parametric amplifiers with quadratic and cubic nonlinearities [52], regular and chaotic vibrations with time delay [53], and frequency comb responses [54].…”

Mechanical overtone frequency combs

“…The ideas behind this field began in nonlinear dynamics, where it was realized that mixing in coupled oscillators may lead to a series of sidebands 14 , which can be regarded as a frequency comb if there exists a fixed phase relation 12 between these sidebands. Experimental demonstrations have shown mechanical frequency combs exist in different mechanical systems 10,[15][16][17][18][19][20][21][22][23] , and have explored connections to well-known concepts in nonlinear dynamics such as bifurcations 15,18,24 , 3-or 4-wave mixing 14,17,25,26 , and symmetry-breaking 27 . The fixed frequency and phase relation between the comb teeth allows the application of techniques known from optical combs.…”