Nonlinear Dynamics

, Volume 92, Issue 4, pp 1955–1974 | Cite as

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

  • A. DolevEmail author
  • I. Bucher
Original Paper


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.


Parametric amplifier Perturbation methods Tunable system Optimization Principal parametric resonance Combination resonance 



The first author would like to acknowledge the generous financial support of the Israeli Ministry of Science, Technology and Space for the Applied science scholarship for engineering Ph.D. students.

Compliance with ethical standards

Conflict of interest

Both authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dynamics Laboratory, Faculty of Mechanical EngineeringTechnionHaifaIsrael

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