Two microcantilever designs: lumped-parameter model for static and modal analysis

This paper develops a lumped-parameter analytical model to enable static load-deformation and modal analysis for two microcantilever designs that can be utilized in mass detection and AFM applications. The circularly filleted microcantilever is currently utilized in several applications, whereas the elliptically filleted configuration is novel. Closed-form compliance/stiffness equations are derived for both microcantilevers in lumped form to permit design in the static regime for both long and short members. Lumped effective inertia fractions are also formulated for the two designs and used in conjunction with the lumped stiffness fractions to quantify the modal response. It is thus possible to tune the static and modal responses of these specific microcantilever designs by geometry alterations. The analytical equations are confirmed through limit calculations, finite element simulation, and experimental results available in the literature.