Equivalent mechanical boundary conditions for single layer graphene sheets

Abstract

To describe and analyse mechanical structures due to external loads, equation of motion must be supplemented with appropriate boundary conditions. When nanomechanical structures (especially layered systems) are considered, satisfying the boundaries is more challenging. It may be essential to develop a specific methodology for any system in such scale and configuration. This work introduces a general approach for boundary conditions of monolayer graphene sheets as the most important part of future sensors and resonators in nanoelectromechanical systems. Comparing with the experiments, it has been demonstrated that the graphene sheets on the adhesive surfaces should be assumed as a hinged edge condition and not as a clamped one. As a result, inaccuracy of the commonly used rigid base as a clamped condition is proven due to comparison with a reported experiment. It is suggested that a flexible substrate can be replaced to have better accordance. A flexible silicon base with equilibrium distance equal to s = 2.5 Å and depth of potential well equal to ε = 0.02 eV is obtained as the best substrate for a square graphene sheet under doubly clamped edge conditions.