Mode shift detection of coupled resonators through parametric resonance and its application to mass sensing

The eigenmode shift in weakly coupled resonators is used for ultra-sensitive micro-mass measurements. For operation in viscous environments, positive velocity feedback is often applied to compensate for the damping effect on the resonators. In the feedback, the real-time sensing of the displacement or velocity of the resonators is essential and in downsizing, a relatively large noise produced in a specific sensor for the velocity or displacement of the resonator may degrade the detection of the mode shift. In this study, we propose using parametric resonance to detect the mode shift without feedback control. Applying the harmonic balance method to an analytical model of coupled cantilevers, we clarify the unstable parameter region in which the resonators are parametrically excited with the first or second eigenmode. We also experimentally confirm without a special environment such as high vacuum, i.e., in air, that the parametrically excited coupled cantilevers produce a highly sensitive mode shift depending on the added mass. The sensitivity of the proposed method is increased by a factor of about 10^3 in the first mode and 10^2 in the second mode compared with the sensitivity in the conventional method based on the natural frequency shift of a single resonator.