Development of analytical models of T- and U-shaped cantilever-based MEMS devices for sensing and energy harvesting applications

Dynamic-mode cantilever-based structures supporting end masses are frequently used as MEMS/NEMS devices in application areas as diverse as chemical/biosensing, atomic force microscopy, and energy harvesting. This paper presents a new analytical solution for the free vibration of a cantilever with a rigid end mass of finite size. The effects of both translational and rotational inertia as well as horizontal eccentricity of the end mass are incorporated into the model. This model is general regarding the end-mass distribution/geometry and is validated here for the commonly encountered geometries of T- and U-shaped cantilevers. Comparisons with 3D FEA simulations and experiments on silicon and organic MEMS are quite encouraging. The new solution gives insight into device behavior, provides an efficient tool for preliminary design, and may be extended in a straightforward manner to account for inherent energy dissipation in the case of organic-based cantilevers.