Inverse Eigenmode Method for Identifying and Locating Added Mass in Mechanically Diverse Coupled Microresonantor Arrays

This paper summarizes a numerical analysis of an eigenmode-based approach for ultrasensitive mass detection via coupled microcantilevers. Mass detection using microcantilevers typically entails the observation of shifts in resonance frequency. Recently, detection systems have been proposed in which multiple cantilever sensors are coupled, either directly or by attachment to a single shuttle mass. Once sensors are coupled, however, mass adsorption on a single sensor alters all eigenmodes of the system. Thus, one disadvantage of the frequency-shift method in such cases is the need for strong mode localization, such that the shift of a single frequency can be associated with a mass change on a specific sensor. The consequent requirement for weak coupling limits the number of microcantilevers that can occupy a specific frequency band. The proposed eigenmode-based detection scheme involves solving the inverse eigenvalue problem to identify added mass, and can be used in cases where more than one eigenfrequency has shifted significantly. The method requires a single measured mode shape and corresponding natural frequency, selected from among those where a shift was observed. The fidelity of the identification of added mass and its location depends on the ability to accurately measure the mode shape, and on the amplitude with which each cantilever vibrates in the chosen mode (in modes without strong localization, multiple cantilevers respond with significant amplitude). Simulation results are presented that quantify, as a function of measurement noise, the ability of the method to accurately identify the cantilever(s) where mass adheres. In cases in which the resonance frequency-shift method is inappropriate due to non-localized modes, the inverse eigenvalue method proposed here can be used to identify both the amount and location of the added mass.