Internal resonance in coupled oscillators – Part II: A synchronous sensing scheme for both mass perturbation and driving force with duffing nonlinearity

Abstract

This paper, the second of two companion papers, mainly reports a synchronous sensing scheme for both mass perturbation and driving force, via the internal resonance phenomena in various coupled Duffing oscillators. The mass perturbation, applied on the low frequency oscillator, is sensed by the dip frequency of the low frequency oscillator caused by modal interaction, and further detected by the corresponding multiplied response frequency of the high frequency oscillator, while the driving force, applied on the low frequency oscillator, is directly detected by measuring the multiplied jump frequency of the high frequency oscillator. A magnetically coupled orthogonal beams with a frequency ratio of two to one, is taken as an example for both theoretical and experimental demonstration. The results show that the synchronous sensing of both mass perturbation and driving amplitude are achievable with a mass sensitivity of −21.5 Hz/g in the range of 0 mg to 314 mg and a force sensitivity of 8.84 Hz/V in the range of 0.5 V to 2.0 V. Compared to the double amplification mass sensing one proposed in the companion paper, the output voltage, the mass sensing range, and the anti-driving fluctuation performance of the proposed scheme in this paper, are improved or amplified by about 167%, 388%, and 3470% times respectively. It is thus more universal and applicable to various micro and nano resonators, when the Duffing nonlinearity is practically considered.