Stable periodic oscillations in simple parallel-plate MEMS based on a family of graphene-like materials

In this paper we study the existence, multiplicity and the stability properties of lateral (positive) periodic oscillations in a class of simple parallel-plate MEM devices based on graphene and graphene-like materials with a non-constant T-periodic input voltage, which are modeled by Duffing equations. We also complete some partial results previously obtained in Kadyrov et al., (2021) for this kind of models and show analytically the existence of a positive asymptotically locally stable T-periodic oscillation, in particular for the graphene-based model. These results could be an approach to a design principle for stabilizing the device without an external controller by means of a tuning of the input voltage. Numerical continuation and simulations are also provided in order to illustrate theoretical results and to reveal the robustness of the graphene-based MEMS compared to the traditional ones.