Multi-channel mass sensing based on multiple internal resonances in three electrostatically coupled resonators

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.