Effect of Graphene Layers on Static Pull-in Behavior of Bilayer Graphene/Substrate Electrostatic Microactuators

A closed-form solution is obtained for the pull-in instability of curved multilayer graphene/substrate microcantilever electrostatic actuators. The first-order fringing-field correction and the interlayer shear between neighboring graphene layers (GLs) and between the graphene and the substrate are incorporated into the analytical model. In the solution procedure, the governing fourth-order differential equation of variable coefficients is converted into a Fredholm integral equation. The resulting equation is solved for the static pull-in voltages by adopting the first natural mode of the cantilever beam as a deflection shape function. The influence of GLs on the pull-in voltages of the electrostatic microactuators is investigated. It is found that laying 10, 30, and 60 GLs on top of the substrate results in increases of about 95%, 190%, and 295%, respectively, in the pull-in voltage of the straight bilayer graphene/substrate electrostatic microactuators. It is also observed that the classical Euler-Bernoulli beam theory fails to predict the pull-in voltages of the multilayer graphene/substrate electrostatic microactuators, showing that the pull-in voltage is highly affected by the graphene interlayer shear.