Internal Resonance Phenomena in Coupled Ductile Cantilevers With Triple Frequency Ratio–Part I: Experimental Observations

Abstract

This paper, the first of two companion papers, mainly reports the experimental observations of the internal resonance in a coupled ductile cantilever system from the viewpoint of mass sensing, mass perturbation effect on coupling tongues, and coupling strength effect on the non-linear vibration. In the coupled ductile cantilever system, two geometrically different Cu-based cantilevers, with a frequency ratio of three to one, are coupled by a coupling overhang. A new flow is proposed to determine the bifurcation points (boundary) of coupling range, which is believed to be more suitable for mass sensing under high energy dissipation circumstance. On one hand, the enlargement of the coupling range is founded to be with the increased exciting force, and the lateral leftward shifting of the coupling tongue is observed with increasing the mass perturbation or lengthening the coupling overhang. On the other hand, the enhancement of the coupling strength, by lengthening the coupling overhang, can make the resonant frequency ratio close to the integer one, decrease the area variation of the coupling tongue with mass perturbation, and improve the linearity of mass sensitivity. This implies that the stability of the coupled system might be improved by enhancing the coupling strength. While a mass sensitivity-amplified scheme and its mechanism will be discussed in Part II.