Nonlinear vibrational analysis of single-layer graphene sheets

Abstract

Recent experiments have shown the applicability of single-layer graphene sheets (SLGSs) as electromechanical resonators. Existing theoretical models, based on linear continuum or atomistic methods, are limited to the study of linear vibrations of SLGSs. Here we introduce a hybrid atomistic-structural element which is capable of modelling nonlinear behaviour of graphene sheets. This hybrid element is based on an empirical inter-atomic potential function and can model the nonlinear dynamic response of SLGSs. Using this element, nonlinear vibrational analysis of SLGSs is performed. It is shown that the nonlinear vibrational analysis of SLGSs predicts significantly higher fundamental frequencies. Also, the effects of vibration amplitude as well as the geometry of the SLGSs on the fundamental frequency are studied and predictive relations between the fundamental frequency, the SLGS length and the non-dimensional vibration amplitude are presented. The results are verified with experimental observations and are in remarkable agreement.

The effect of local bending on gating of MscL using a representative volume element and finite element simulation

“…[22][23][24][25] However, first, it is important to define how the proper equivalent mechanical properties of the proposed RVE can be determined based on physical behavior of the target structure. In the case of MscL, we modeled the initial shape of the RVE based on the MscL crystal structure in the detergent.…”

Nonlinear vibration behavior of graphene resonators and their applications in sensitive mass detection

“…However, a recent study by Isacsson et al [19] has only concentrated on the harmonic oscillation of a graphene resonator, even though a graphene resonator can easily reach the nonlinear vibration regime. To the best of our knowledge, despite recent studies [28,29] theoretically reporting the nonlinear vibration of a graphene resonator, the nonlinear oscillation of a graphene resonator (particularly, nonlinearity tuning), as well as atomic mass detection using graphene-based nonlinear oscillators, has not been well studied based on a continuum elastic model and/or MD simulation.…”

Transverse vibration of single-layer graphene sheets

“…The out-of-plane deformation of SLGS has been considered using the continuum mechanics models [13,22], together with continuum and truss-like structural assemblies [23][24][25][26][27][28][29][30]. In a recent paper a nonlinear mechanical model has been used [31] to take account for large deformations in SLGS. They observed higher resonance frequencies from the nonlinear model compared with the equivalent linear model.…”