Nonlinearity modulation in a mode-localized mass sensor based on electrostatically coupled resonators under primary and superharmonic resonances

Abstract

A general model of a mode-localized mass sensor incorporating two weakly coupled clamped-clamped microbeams under electrostatic excitation is presented, and a reduced-order model considering quadratic and cubic nonlinearities is established. The multiple time scales method is used to solve the dynamic characteristics of the coupled resonators under primary resonance, simultaneous superharmonic and primary excitations, and one-third superharmonic resonance respectively, and to analyze the contribution of each harmonic excitation term. It is shown that the sensor can display softening, hardening, and linear behaviors by tuning the overall nonlinear coefficient in three different excitation scenarios.
Furthermore, the conditions for restoring linear behavior with the highest possible amplitude without any hysteresis under different excitations are obtained. Finally, the mass sensitivities represented by the relative shift of amplitude ratio are calculated for all the resulting dynamic behaviors. The results show that the sensitivity is highest, for the hardening behavior in the in-phase mode and for the softening behavior in the out-of-phase mode. Interestingly, the sensitivities of the linear behavior obtained by nonlinearity modulation are the same for the two vibration modes, which is improve the output stability. Consequently, the sensor resolution can be significantly enhanced below the pull-in instability, while avoiding noise mixing.

Nonlinear dynamic morphing of conical bistable dielectric elastomer actuator

“…Bistable structures are characterized by having two stable positions with minimum potential energy, as well as one unstable position with maximum potential energy within their stroke range. As a result, bistable structures have applications in various fields, including micro-electromechanical systems [1][2][3], switch [4][5][6], relays [7], and space collapsible mechanisms [8]. However, traditional actuation components for stable state transition like motors and pumps often pose challenges in terms of their complex structures and heavy weight.…”

Generalized Analysis of Systems Based on Two Nonlinear Resonators

“…However, in circuits in which the nonlinearities are not closely connected, the procedure fails. This is the case of circuits containing two nonlinear resonators, which have recently attracted interest for a variety of applications, including nonlinear isolators [19], [20], [21], [22], [23], robust wireless power transfer [24], [25], and sensors [26], [27], [28], [29], [30], [31]. The multivalued solution may originate in either one or another resonator or be the result of the combined action of both.…”