Autoparametric Internal Resonance in Coupled Oscillator: An Excitation Amplitude Insensitive Mass Sensing Scheme With a Roof Tilting

Abstract

To overcome the effect of slowly changing excitation amplitude caused by temperature drift etc. on sensing performance, a slope-based working mechanism is exploited in autoparametric internal resonance systems. Through increasing modal damping, energy transfer between coupled modes is observed to be decreased, and the depressed cave on the amplitude response curve transits to a flat roof that is independent of both excitation amplitude and excitation frequency. A theoretical expression is established to characterize the flat roof, which tends to tilt when applying mass perturbations. The slope of the flat roof is found to be independent of the excitation amplitude but a function of the applied mass perturbations, while the frequency range of which broadens or narrows with the increase or decrease of the excitation amplitude respectively. Further concerning on the slopes under different excitation amplitudes, results from numerical study is also basically consistent with those from the theoretical prediction, apart a maximum relative deviation about 8%. An excitation insensitive mass sensing scheme via flat roof tilting is thus proposed. With applying different mass perturbations, the proposed scheme is mutually confirmed by both theoretical and numerical results, featured with a high linearity in a certain mass range. Compared to conventional frequency shift based or amplitude change based one, the proposed sensing scheme is insensitive to slow change of excitation amplitude, and is believed to have great potential in engineering scenarios with varying environmental temperature.