The nonlinearity cancellation phenomenon in micromechanical resonators

Abstract

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr.Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.

Design and fabrication of a novel resonant surface sensitive to out-of-plane forces for the indentation and injection of living cells

“…Fig.10 confirms the linear vibrations of the structure since the curve is not distorted by hysteresis. Indeed, the small reported oscillation amplitude prevented the occurrence of nonlinearities such as spring softening or spring hardening effects [15]. Fig.…”

Pull-In Retarding in Nonlinear Nanoelectromechanical Resonators Under Superharmonic Excitation

“…The expressions of Eqns. (28) and (29) are quite large. For the sake of conciseness, they are not detailed here…”

“…For the primary resonance of a clamped-clamped mi- crobeam, A c is defined as the oscillation amplitude for which the equation dΩ dβ = 0 has a unique solution β c = 2π 3 [27]. It was also shown analytically and experimentally [7,28] that the critical amplitude for micromechanical clamped-clamped beam resonators under primary resonance is only determined by the beam thickness h in the direction of vibration and the quality factor Q. The question is whether or not the critical amplitude of a NEMS resonator is invariant with respect to the excitation.…”

“…In order to explain how to deduce the mechanical critical amplitude from Eqns. (28) and (29), we assume the simplified case of neglected nonlinear electrostatic effects…”

Nonlinear tuning of microresonators for dynamic range enhancement

“…More recently, nonlinear tuning has been used to increase the dynamic range of electrostatically driven resonators [37][38][39] (but see also [40] for an example of relying on modal coupling). The need for analytical or computational schemes for finding critical values at which the transition to the nonlinear regime occurs has been highlighted by several authors [33,38,41,42].…”