Internal resonance in coupled oscillators – Part I: A double amplification mass sensing scheme without Duffing nonlinearity

This paper, the first of two companion papers, mainly reports a double amplification scheme for mass sensitivity, via a differential phenomenon in various non-Duffing internal resonance systems with even power nonlinearities and coupling. Both frequency sum and amplitude difference of the two symmetrical peaks, in response amplitude of the basic mode, are capable of differentially amplifying the sensitivity as well as greatly suppressing the effect of noise caused by driving amplitude fluctuation. Combining frequency up-conversion to further amplify the sensitivity, double amplified mass sensitivity is thus achieved via frequency shift. Magnetically coupled orthogonal beams with a frequency ratio of two to one, is adopted as an example for both theoretical and experimental demonstration. Experimental results show effect of driving voltage fluctuating in the range of 200 mV to 600 mV is reduced by 360%, as well as the sensitivity for mass perturbation in the range of 0 g to 10 g is 332% amplified. Lower driving threshold and wider sensing range are further obtained through adjusting modal damping. Compared to those based on synchronization or internal resonance under the same frequency ratios, the proposed amplification scheme, not only enhances the mass sensitivity up to about 166%, but also suppresses the effect of driving amplitude fluctuation down to about 27.8%, indicating a potential possibility to break through the sensing limit.