Small scale effect on the pull-in instability and vibration of graphene sheets

Abstract

In this paper, the small scale effect on the pull-in instability and frequency of graphene sheets subjected to electrostatic and van der Waals forces is studied. Eringen's nonlocal elasticity theory is used to account for the small scale effect, and the graphene sheet is modeled as a nonlocal plate. Reduce-order model incorporating nonlocal effect and van der Waals force is derived. Results show that nonlocal elasticity reduces the pull-in voltages and fundamental frequencies. The effect of nonlocal parameter on pull-in voltages and fundamental frequencies is more obvious if the size of nanoplate is smaller. In addition, an empirical formula for pull-in voltage is explored. The form of the empirical formula is relatively simple, therefore is convenient for engineers to indicate an experimental method to determine the nonlocal parameters of the materials and to design nano-switches.