Localization in coupled systems: Part II — Consideration on damping issue in a mode-localized cantilever array

Abstract

The use of vibration mode localization in arrays of mechanically-coupled, nearly identical cantilevers has been studied for ultra-sensitive mass detection and analyte identification. The effects of geometrical design of the coupling overhang, cantilever length, as well as the number of identical coupled cantilevers on the magnitude enhancement with a small mass perturbation were previously reported in DTIP 2011. This paper however, analytically investigates the effect of material damping, induced by the internal friction loss, on energy confinement in a mode-localized three-cantilever array. Firstly, the material damping will not change three typical eigenstates of the array. Therefore, the proposed three-cantilever array can be applied to mass detection and analyte identification as well. Secondly, the sensitivity of mass sensing with the proposed array declined from 22990.70 to 33.56 because of the decrease in amplitude values caused by energy loss. It is the material damping that brings about the energy loss that influences the spatial propagation confinement of vibration. Additionally, experimental verification will be conducted in our future work.