Continuum elastic modeling of graphene resonators

TL;DR

This paper develops and validates continuum elasticity models for graphene resonators, showing that nonlinear effects are essential for accurate static and dynamic predictions, with Duffing equations effectively capturing membrane dynamics.

Contribution

It introduces simplified continuum models derived from atomistic data for graphene, validated through numerical analysis of resonator responses, highlighting the importance of nonlinearities.

Findings

Nonlinearities are significant for deflections around 0.5 Å.

Coupled Duffing equations can accurately model graphene membrane dynamics.

Continuum models are validated against atomistic-based simulations.

Abstract

Starting from an atomistic approach we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated. We find that already for deflections of the order of 0.5{\AA} a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes.