Optimizing the dynamical behavior of a dual frequency parametric amplifier with quadratic and cubic nonlinearities

TL;DR

This paper introduces a novel dual-frequency parametric amplifier using quadratic and cubic nonlinearities, which enhances weak signals in mechanical oscillators by tunably controlling feedback and excitation signals.

Contribution

It presents a new optimized nonlinear resonator design that improves signal sensitivity and response control through dual nonlinear feedback tuning.

Findings

Enhanced signal amplification with tunable nonlinear feedback.

Nearly linear response achieved through cubic and quadratic feedback tuning.

Effective amplification for weak signals in rotating structures.

Abstract

The paper describes a novel parametric excitation scheme that acts as a tunable amplifier by controlling two pumping signals and two nonlinear feedback terms. By modulating the stiffness of a mechanical oscillator with a digital signal processor, low frequency inputs are projected onto a higher resonance frequency, thus exploiting the natural selective filtering of such structures. Described is an optimized dual-term nonlinear stiffness resonator that enhances the input signal level and the sensitivity to changes in both amplitude and phase, while limiting the obtained response to desired levels. This amplifier is geared to cases when the frequency of the input is known or measurable, like in rotating structures, while the amplitude and phase are too weak to be detected without amplification. It is shown that by tuning the cubic and quadratic feedback terms, the amplifier benefits from a nearly linear response behavior, while exploiting the benefits of nonlinear and pumping signal enhancements.