Parametric amplification in a torsional microresonator

Carr, Dustin W.; Evoy, Stéphane; Šekarić, L.; Craighead, Harold G.; Parpia, J. M.

doi:10.1063/1.1308270

Cited by 159 publications

(136 citation statements)

References 10 publications

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“…Above this threshold, the amplitude of the motion grows until it is saturated by nonlinear effects. We shall describe the nature of these oscillations for driving above threshold later, both for the first (n D 1) and the second (n D 2) instability tongues, but first we shall consider the dynamics when the driving amplitude is just below threshold, as it also offers interesting behavior and a possibility for novel applications such as parametric amplification [4,12,57] and noise squeezing [57].…”

Section: Parametric Excitation Of a Damped Duffing Resonatormentioning

confidence: 99%

Nonlinear Dynamics of Nanomechanical Resonators

Lifshitz

Cross

2010

Nonlinear Dynamics of Nanosystems

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Section: Parametric Excitation Of a Damped Duffing Resonatormentioning

confidence: 99%

Nonlinear Dynamics of Nanomechanical Resonators

Lifshitz

Cross

2010

Nonlinear Dynamics of Nanosystems

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“…82,84 Recently, optical interferometry techniques, in particular path stabilized Michelson interferometry and Fabry-Pérot interferometry, have been extended into the NEMS domain. [85][86][87][88][89] Figure 9 shows a typical room temperature optical interferometer setup. In path stabilized Michelson interferometry, a tightly focused laser beam reflects from the surface of a NEMS device and interferes with a reference beam.…”

Section: Type Of Noisementioning

confidence: 99%

Nanoelectromechanical Systems

Roukes¹

2005

Microsystems

100

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Nanoelectromechanical systems ͑NEMS͒ are drawing interest from both technical and scientific communities. These are electromechanical systems, much like microelectromechanical systems, mostly operated in their resonant modes with dimensions in the deep submicron. In this size regime, they come with extremely high fundamental resonance frequencies, diminished active masses, and tolerable force constants; the quality ͑Q͒ factors of resonance are in the range Q ϳ 10 3 -10 5 -significantly higher than those of electrical resonant circuits. These attributes collectively make NEMS suitable for a multitude of technological applications such as ultrafast sensors, actuators, and signal processing components. Experimentally, NEMS are expected to open up investigations of phonon mediated mechanical processes and of the quantum behavior of mesoscopic mechanical systems. However, there still exist fundamental and technological challenges to NEMS optimization. In this review we shall provide a balanced introduction to NEMS by discussing the prospects and challenges in this rapidly developing field and outline an exciting emerging application, nanoelectromechanical mass detection.

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“…The 4th order Runge-Kutta method is used to integrate the set of Eq. (6). A small integration step (2π/200) has to be chosen to ensure a stable solution and to avoid the numerical divergence at the points where derivatives of F e and F s are discontinuous.…”

Section: Bifurcation and Chaos Behaviormentioning

confidence: 99%

“…Carr et al [6] and Zalalutdinov et al [7] studied the parametric amplification of the motion of resonators through electrostatic and optical actuation. However, the reported methods should be used to discuss the instability and control strategies.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

Zhang

Meng

Wei

2010

Shock and Vibration

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Abstract. In this paper, nonlinear dynamics and chaos of electrostatically actuated MEMS resonators under two-frequency parametric and external excitations are investigated analytically and numerically. A nonlinear mass-spring-damping model is used to accounting for squeeze film damping and the parallel plate electrostatic force. The micro-structure is excited by a dc bias electrostatic force and a harmonic force with a frequency tuned closely to their fundamental natural frequencies (combination oscillation). The quality factor is calculated for the microcantilever beam of the resonator considering squeeze film damping. The effect of nonlinear squeeze film damping on the frequency response, quality factor, resonant frequency and nonlinear dynamic characteristics of the dynamic system are provided with numerical simulations using the bifurcation diagram, Poicare maps, largest Lyapunov exponent and phase portrait. The results show that the dynamic system goes through a complex nonlinear vibration as the system parameters change. It is indicated that the effect of nonlinear squeeze film damping should be considered due to its decreasing the quality factor and changing the nonlinear phenomena of the MEMS resonators.

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Parametric amplification in a torsional microresonator

Cited by 159 publications

References 10 publications

Nonlinear Dynamics of Nanomechanical Resonators

Nonlinear Dynamics of Nanomechanical Resonators

Nanoelectromechanical Systems

Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

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