Topology dependence of mass sensitivities in mode-localized sensors

Vibration mode localization has been employed as an ultrasensitive approach for mass detection and identification in recent years. Sensitivity enhancements of nearly three orders of magnitude relative to the more conventional resonant frequency shift approach have been experimentally demonstrated using this sensing paradigm, by either exploiting the critical dependence of the parametric sensitivity on the strength of internal coupling or by increasing the number of degrees of freedom by arraying multiple resonators with weak coupling springs. We propose here, for the first time, an additional approach to sensitivity enhancement in such mode-localized mass sensors by utilizing the sensitivity dependence on the operating frequency and the stiffness of the resonator topology. We experimentally demonstrate the sensitivity dependence on the topology, by comparing and contrasting the vibration behaviour of three pairs of electrically coupled microelectromechanical (MEM) resonators of different structural configurations and operating frequencies. The shifts in the eigenstates for the same relative mass additions are experimentally demonstrated to be over three orders of magnitude greater than corresponding resonant frequency shifts. They are also shown to increase proportionally with the square of the resonant frequencies of the coupled resonator platforms (with the stiffer configurations of higher operating frequencies yielding a further one order of magnitude improvement over the more compliant topologies of nearly equal resonator masses). This topology dependence while providing a systematic approach to the design of mode-localized mass sensors within a given design space, also suggests an alternate route to improving the mass sensitivity by designing stiffer topologies with weak coupling instead of the more conventional route of scaling down system dimensions in traditional resonant mass sensors.