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

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.

The effects of nonlinear damping on degenerate parametric amplification

“…Recent theoretical analysis for PA include the effects of quadratic and cubic nonlinearities [7], dualfrequency parametric amplifiers with quadratic and cubic nonlinearities [54], regular and chaotic vibrations with time delay [55], and frequency comb responses [56].…”

Parametrically amplified Mathieu-Duffing nonlinear energy harvesters

“…It is shown that for specic positions of the parametric excitation force and real-time topology modication it is possible to amplify specic inputs in a three degree of freedom system. Coupling between the quadratic and cubic nonlinearities with the dual-frequency parametric amplication model of the Dung oscillator was studied in [32]. Moreover, in [33] a combination of two piezoelectric cantilever beams with magnetic tip masses having direct and parametric excitation is introduced as a model of the EH device.…”

On the response of MEMS resonators under generic electrostatic loadings: theoretical analysis

“…Resonators are commonly excited near primary resonance. However, other excitation methods have been explored recently for various applications [10][11][12][13][14][15][16][17][18][19][20][21].…”

“…Parametric excitation near twice the structure's natural frequencies is among the most common. Parametric excitation has been used in various applications including signal amplification [10,11,19], thermo mechanical noise squeezing [12], and RF filtering [13]. Multi or mixed-frequency excitation has been used as well, in which two or more frequency signals are mixed and applied to the resonator [14].…”

“…Mixed frequency excitation gives birth to interesting behaviors, such as the activation of combination resonances, which has been reported for applications in micro computing [15]. Multi-frequency parametric excitation has also been investigated, where the influence of one or more external excitation is studied along with simultaneous parametric excitation [16][17][18] or multiple simultaneous parametric excitations [19].…”