Understanding mechanical domain parametric resonance in microcantilevers

In this paper we present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular illustrate that parametric resonance phenomena occur in capacitively actuated micro-cantilevers. The combined parametric/harmonic mode of operation is investigated as well and experimental data are provided.