Inertial mass sensing with low Q-factor vibrating microcantilevers

Mass sensing using micromechanical cantilever oscillators has been established as a promising approach. The scientific principle underpinning this technique is the shift in the resonance frequency caused by the additional mass in the dynamic system. This approach relies on the fact that the Q-factor of the underlying oscillator is high enough so that it does not significantly affect the resonance frequencies. We consider the case when the Q-factor is low to the extent that the effect of damping is prominent. It is shown that the mass sensing can be achieved using a shift in the damping factor. We prove that the shift in the damping factor is of the same order as that of the resonance frequency. Based on this crucial observation, three new approaches have been proposed, namely, (a) mass sensing using frequency shifts in the complex plane, (b) mass sensing from damped free vibration response in the time domain, and (c) mass sensing from the steady-state response in the frequency domain. Explicit closed-form...