The nonlinear dynamics in micro/nano electromechanical sensor have attracted a myriad of attention of researchers due to its great potential to improve sensors’ performance In this paper, a novel mass sensor exploiting the bifurcation phenomenon in parametrically excited mode-localized resonators is proposed. The mathematical model is established by Euler-Bernoulli theory and solved by the method of multiple scales. Meanwhile, the harmonic balance method combined with asymptotic numerical method is utilized for validation. The dynamics and bifurcation topology of the sensor are investigated and the potential of mass sensing on bifurcation point is explored. Compared to relative shift of frequency, the sensitivity in terms of relative shift of amplitude ratio can be enhanced by 4 orders of magnitude. Finally, the effects of coupling voltage are studied which shows that the sensitivity can be further improve with the decrease of coupling voltage above the mode aliasing.

Multiple internal resonances in three electrostatically coupled microbeams have been theoretically investigated and were utilized to multi-channel mass detection. The frequency ratio among the three electrostatically coupled resonators of different sizes can be tuned to satisfy the specific conditions for multiple internal resonances. A reduced order model considering quadratic nonlinearity and frequency commensurability is established, and solved by the method of multiple scales, and verified by the harmonic balance method combined with the asymptotic numerical method. The nonlinear dynamics involving pitchfork and saddle-node bifurcations were analyzed and utilized to detect single, dual, or even multiple masses simultaneously. The frequency shift of the bifurcation points or the amplitude shift of a specific operating frequency near the bifurcation point were introduced as an output sensitivity. And then, a multi-channel single output detection mechanism was proposed, in addition to a single mass detection, the proposed sensor enables dual or even multi-channel mass detections based on frequency and amplitude shifts of pitchfork and saddle-node bifurcation points of the coupled and uncoupled vibration states. Furthermore, the effects of driving and coupling voltages on the dynamic response of the system were obtained. This work not only proposes a new way for multi-channel mass detection, but also provides technical support for multi-channel detection of other signals.

A general model of two resonators subjected to electrostatic coupling and simultaneous primary and superharmonic excitations is developped. A reduced-order model including quadratic and cubic nonlinear terms is generated and the multi-scale method is used to solve the dynamic characteristics and analyze the contribution of the different frequency components. In addition, an overall nonlinear coefficient is defined, which can be adjusted to make the system exhibit different dynamic characteristics including softening, hardening, and linear behaviors. Finally, the conditions for restoring the linear behavior at the highest possible amplitude and suppressing its hysteresis are given.