The nano/microelectromechanical systems (N/MEMS) have gained considerable attention in the past few decades for their attractive properties such as small size, high reliability, batch fabrication, and low power consumption. Carbon‐based nanostructures such as one‐dimensional carbon nanotubes (CNTs) and two‐dimensional graphene are the key materials in many N/MEMS and very attractive due to their unique properties and ultra‐small dimensions especially the large surface area‐to‐volume ratio make them prime candidates for sensing applications in N/MEMS. Therefore, the main objective of this manuscript is to analyze the dynamic behavior of a graphene N/MEMS. The mathematical model of this system uses constitutive stress–strain law and the electrostatic Coulomb force for the restoring force of the spring and the driving force of the mass attached to the spring, respectively. The modeled system is then solved by employing the variational iteration method (VIM) accompanied by the techniques of the Laplace transform. This coupling of VIM and Laplace transform (Laplace‐based variational iteration method [LVIM]) not only suggests an easier approach to determine the Lagrange multiplier used in the VIM but also provides approximate nonlinear frequency and approximate solution of graphene N/MEMS in an efficient way. Moreover, the LVIM also approximates the pull‐in threshold, a critical phenomenon associated with N/MEMS, in terms of model parameters. Finally, to verify the obtained findings, the results are compared with those achieved numerically as well.
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