Frequency Superposition of Coupled Modes via Autoparametric Vibration for Ultrasensitive Mass Detection

Abstract

An ultrasensitive mass detection scheme is proposed via frequency superposition phenomena of autoparametric vibration systems (AVSs) for the first time in this article. For an AVS, the amplitude–frequency curve of the direct excitation mode (DEM) contains two symmetrical peaks, due to the energy transfer with the parametric excitation mode (PEM). We have discovered that the frequency superposition of the two coupled modes can be realized via frequency sum of the two peaks. After applying mass perturbation, both the two peaks shift to lower frequencies, and sum of their frequency shifts is equal to the sum of the modal frequency shift of the PEM and twice that of the DEM. To evaluate quantitatively the sensing performances, frequency expressions of the two peaks have been theoretically derived, as well as the mass sensing theory has been established. Both theoretical and numerical results show that the frequency shift is about 1.5 times multiplied, as well as high stability and high linearity are obtained. Compared to the conventional frequency shift-based scheme, not only the mass sensitivity can be amplified by 50% but also the effect of the excitation fluctuation can be greatly suppressed. This work not only opens a new avenue in applications of AVSs but also provides a new metrological scheme for mass sensitivity amplification.