Five parametric resonances in a microelectromechanical system

Nonlinear Dynamics of Nanomechanical Resonators

“…Solid curves indicate stable solutions, and dashed curves are solutions that are unstable to small perturbations. Thin curves show the response without nonlinear damping (η D 0), which grows indefinitely with frequency Ω P and is therefore incompatible with experimental observations [8,66,71] as well as the assumptions of our calculation. As we saw for the saturation below threshold, without nonlinear damping and with linear damping being small, one would have to go to higher orders of perturbation theory to search for a physical mechanism that could provide saturation.…”

“…One can show [42] that there is a sequence of tongue shaped regions in the H ω P plane where the smallest fluctuations away from the quiescent state of the swing, or any other parametrically-excited resonator [66], are exponentially amplified. This happens when the amplitude of the modulation H is sufficiently strong to overcome the effect of damping, where the threshold for the nth instability tongue scales as (Q 1 ) 1/ n .…”

“…The simplest and probably most commonly used on the micron scale is to use an external electrode that can induce an external potential. If the external potential is modulated in time it can change the effective spring constant of the resonator [24,51,52,66,71,72]. Based on our treatment of this situation in Section 8.1.3, this method is likely to modulate all the coefficients in the potential felt by the resonator, thus also modulating, for example, the Duffing parameter α.…”

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

“…It is necessary to benefit from the parametric amplification phenomena which had not remarked. A demonstration of the phenomena of parametrically excited vibrations in MEMS/NEMS was reported in [8,17]. Abdel-Rahman and Nayfeh [9] and Gallacher et al [10] applied the super-harmonic and combination parametric resonances as suitable excitation methods to minimize electrical "feedthrough".…”

Signal amplification through bifurcation in nanoresonators

“…These include parametric amplification, and squeezing of classical and quantum noise [1], generation of entangled pairs of photons [2], and effective actuation of micro-and nanomechanical resonators [3][4][5]. Our previous investigations of the parametric excitation of coupled nanomechanical resonators [6,7] have led to the discovery of a novel and generic amplification mechanism.…”