On the Sensitivity Analysis of Mode-Localized Sensors Based on Weakly Coupled Resonators

Abstract

Purpose: This work investigates the mode veering and mode localization behavior of a coupled micro-cantilever system with mass disturbances. A new sensitivity metric is defined based on the difference between the absolute values of amplitude ratios for mass sensing in mode-localized sensors.Methods: Numerical and finite element method (FEM) analyses are conducted to validate the corresponding analytical results for the undamped modal analysis. In addition, the derived sensitivity is also verified by the FEM result of the damped harmonic responses. Finally, an experimental study is conducted to qualitatively validate the theoretical and numerical results.Results: The derived sensitivity shows a good agreement with the numerical and FEM results for the modal analysis and damped harmonic responses. The experimental results show the same trend observed in the theoretical and finite element results. The derived sensitivity possesses a superior linearity in the full disturbance range with high precision. The influence of the damping and coupling factor on the resolution of mass sensing is also unveiled.Conclusions: The superior linearity and effectiveness of the proposed sensitivity metric is confirmed, which has a full scope of application and high precision compared to the conventional sensitivities. The derived sensitivity is proved to be applicable for the damped harmonic response analysis as well. This work also reveals that there is a trade-off between the sensitivity and resolution when selecting the coupling factor.