Dynamics of mechanically and electrostatically coupled microcantilevers

In this paper we study the behavior of a pair of electrostatically and mechanically coupled microcantilevers. For the case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are governed by a pair of coupled Mathieu equations. We provide experimental evidence that confirms the validity of the mathematical model proposed, including in particular a mapping of the first order coupled parametric resonance region. The mechanical coupling coefficients are identified from experimental data, and their values are shown to match well those obtained by finite element methods.