Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators View Full Text


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Article Info

DATE

2016-01-20

AUTHORS

Sebastián I. Arroyo, Damián H. Zanette

ABSTRACT

We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled – contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators – and, in particular, micromechanical oscillators – provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve, and provide analytical approximate expressions for the time dependence of the oscillation amplitude and frequency during transients. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices. More... »

PAGES

12

References to SciGraph publications

  • 1990. Feedback Stabilization of Nonlinear Systems in ROBUST CONTROL OF LINEAR SYSTEMS AND NONLINEAR CONTROL
  • 2012-01. Frequency stabilization in nonlinear micromechanical oscillators in NATURE COMMUNICATIONS
  • 1984. Chemical Oscillations, Waves, and Turbulence in NONE
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    http://scigraph.springernature.com/pub.10.1140/epjb/e2015-60517-3

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    http://dx.doi.org/10.1140/epjb/e2015-60517-3

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