Optimal design and system characterization of graphene sheets in a micro/nano actuator

Abstract

In this article, an element free Galerkin method (EFGM) is used for dynamic characterization of a capacitive nanoactuator as subjected to a DC voltage by using a proposed nonlocal plate theory. The system governing equations of an electrostatic nanoactuator are first derived based upon the theory of nonlocal Kirchhoff plate. The intermolecular forces, such as Casimir and van der Waals forces, are included in the proposed model. The weak form representation of equilibrium equations is presented based on Hamilton principle and a discrete moving least squares (MLS) approximation for the shape function. Since the MLS approximation does not satisfy the principle of Kronecker delta, a penalty method is then imposed upon to equip as auxiliary boundary conditions. The discrete weak form is adopted to solve for eigenvalue solutions and natural frequencies of the plate. Since numerical experimental results indicate that the number of nodes that scattered in the working domain can affect final solutions dramatically, a calibration scheme is introduced into the proposed modeling system beforehand by using some referred known functions. Eventually, the characterization dynamic behaviors for a nanoactuator with designated DC voltage is made possible. The results indicate that the proposed modeling approach and computational program are accurate and feasible for design and system characterization of single-layered graphene sheets (SLGS) by the adjustment of scale effect to allow the associated pull-in voltage of the device to be optimally designated.