Analytical Model for Enhanced Eigen-Mode Sensitivities in a Coupled Micro-Resonator Array for Ultra-Sensitive Mass Measurement

Resonant sensors using coupled micro-cantilever array have applications in a wide range of areas including ultrasensitive mass detection of bio-molecules and chemical analytes. A target mass deposited on one of the cantilevers can be detected by measuring shift in eigen-spectrum. Experimental observations indicate that eigenmodes are more sensitive to mass perturbation than resonant frequencies or eigenvalues. However, analytical works, available in literatures, are limited to only two and three cantilever array for eigenvalue sensitivity and only two cantilever array for eigenmode sensitivity. In the present work, an analytical foundation for estimation of eigenmode sensitivities for a general n-array micro-resonator sensor is developed using matrix perturbation theory. The formulation characterizes the modal spectrum and eigenmode sensitivities as a function of elastic interconnection stiffness parameter and unperturbed eigenmodes. Measurement of added mass is demonstrated for different analyte locations using numerically constructed frequency response function (FRF) curves. Error in measurement is also investigated as a function of interconnection stiffness ratio, position of analyte mass, and selection of particular eigenmode to be measured.