Localization in coupled systems: Part III - vibration characteristics analysis in a mode-localized four cantilever array with and without mass perturbation

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. And the effect of material damping induced by the internal friction loss was studied in DTIP 2017. However, this paper has made an analytical study on mass perturbation in a mode-localized four-cantilever array made of copper, whose amplitude ratio is higher than previous cantilever arrays. In light of vibration eigenstate changes, the sensitivity is higher when mass is applied on the side resonator (NO.1 or NO. 4). The conclusion can be analytically determined by simulation results. To further analyze sensitivity, amplitude ratio between NO.1 and NO.4 resonator (NO.2 and NO.3 resonator) has been investigated. In this paper, the mode-localized cantilever array has a wide range of applications such as in measuring electric field force, magnetic force etc.