Internal Resonance Phenomena in Coupled Ductile Cantilevers With Triple Frequency Ratio-Part II: A Mass Sensitivity Amplification Schemes

Abstract

This paper, the second of two companion papers, reports a mass sensitivity amplification scheme, via amplitude and frequency shift enhancement of internal resonance (IR) in coupled ductile cantilevers with frequency ratio of three to one. The amplitude enhancement of super-harmonic resonance of order three in short cantilever can be achieved by the coupling of long cantilever via coupling overhang through the internal resonance between the low frequency mode and the high frequency mode. Such kind of enhancement mechanism is clarified by both experimental verification and numerical analysis. While the frequency shift enhancement of coupled cantilevers are experimentally demonstrated by comparatively analyzing the frequency shifts of single-cantilevers and coupled cantilevers with varying mass perturbations. The impact of coupling strength on frequency shifts of coupled cantilevers is also studied. The proposed scheme with coupled IR ductile cantilevers, can accomplish “sensing and detecting separation,” “amplitude and frequency shift enhancement,” and the linearity improvement of mass detecting, which is expected to be applicable to ultimate sensing of mass, force, field, and any other external perturbations, even under an atmospheric environments.