Modeling, design, and characterization of multisegment cantilevers for resonant mass detection

The work presents the analytic modeling, design, and the experimental and numerical characterization of multisegment cantilevers' bending and torsion resonant responses with the aim of evaluating the amount and position of matter which deposits on these elastic structures. The cantilevers may comprise any number of geometrically different segments that are serially connected, and actual results are presented for the two-segment, circularly notched configuration. The generic analytical model, which formulates the bending and torsion resonant frequencies of both the original cantilever and the one with the attached mass, is derived by means of Rayleigh's quotient approach. Relationships are formulated between nondimensional parameters characterizing the geometry, resonant frequencies, and deposited mass amount and position for both bending and torsion. The sensitivity of the frequency shift to the landing parameters and mass amount are also studied. Analytical model, finite element, and experimental testing data corresponding to the bending and torsion resonant responses of macro- and nano-two-segment, circularly notched cantilever specimens are in agreement. The analytical model of the circularly notched cantilever is further employed to investigate the relationships between the cantilever geometry parameters, the deposited mass amount, and its landing position to the change in the bending and torsion resonant frequency.