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

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.