A review of parametric resonance in microelectromechanical systems

Moran, Kari M.; Burgner, Christopher; Shaw, Steven W.; Turner, Kimberly L.

doi:10.1587/nolta.4.198

Cited by 30 publications

(20 citation statements)

References 42 publications

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“…4 by the linear prediction) superposed. The stability boundary takes the shape of an Arnold's tongue404142 as previously observed in nanomechanical systems434445. The offset frequency for this data is selected so that the measured gain falls on the theoretical surface.…”

Section: Resultsmentioning

confidence: 99%

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

Nitzan

Zega

et al. 2015

Sci Rep

102

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Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

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Section: Resultsmentioning

confidence: 99%

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

Nitzan

Zega

et al. 2015

Sci Rep

102

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“…In recent years many different electrostatic actuators were used to induce parametric excitation [6]. However, these electrostatic actuators inevitably included additional nonlinear effects, and did not afford a pure modulation of stiffness.…”

Section: B Se Modelmentioning

confidence: 99%

“…In recent decades, significant work has been devoted to utilize nonlinear dynamics in micro-systems, with specific interest in parametrically actuated resonators [6]. Parametric resonators are dynamic systems in which at least one of the physical parameters (i.e.…”

Section: Introductionmentioning

confidence: 99%

A MEMS Implementation of a Classic Parametric Resonator

Shmulevich

Grinberg

Elata

2015

J. Microelectromech. Syst.

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We present a microelectromechanical systems realization of a classic parametric resonator. This parametric resonator is ideal in the sense that the electrostatic stiffness, which may be time modulated, is not affected by motion. We also present a simple, efficient, and intuitive model of parametric excitation. This model predicts the minimal modulation amplitude required to obtain an unbounded response in a parametric system with linear damping. We show experimental results in which the system is operated as a Meissner resonator.[ 2014-0381]Index Terms-Electrostatic actuators, parametric excitation, parametric resonators, tapered comb-drive. 1057-7157

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“…There have been numerous studies on parametric resonance because it is induced by an interesting resonance mechanism that is different from that of external or forced resonance; the steady-state amplitude is essentially determined by the nonlinearity, in particular the cubic nonlinearity, in the system [1] and can be used as a excitation method for highsensitivity micro-nano-resonators [2]. The resonance regions (such as the Arnold tongue and the linear unstable region) investigated by linear analysis correspond to the unstable region of the trivial steady state.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, in order to change the frequency response curve in parametric resonance on demand, we need a novel method by which to change the inherently existing original nonlinearity in the system. Recently, based on the advantageous use of the characteristics of the parametric resonance, which differ from those of the external resonance, the development of high-performance resonators, for use in energy harvesters and mechanical filters, for example, particularly in the field of MEMS, has become very attractive [2,3].…”

Section: Introductionmentioning

confidence: 99%