Vibration of Single- and Double-Layered Graphene Sheets

Abstract

Free vibration of single- and double-layered graphene sheets is investigated by employing nonlocal continuum theory and molecular dynamics simulations. Results show that the classical elastic model overestimated the resonant frequencies of the sheets by a percentage as high as 62%. The dependence of small-scale effects, sizes of sheets, boundary conditions, and number of layers on vibrational characteristic of single- and double-layered graphene sheets is studied. The resonant frequencies predicted by the nonlocal elastic plate theory are verified by the molecular dynamics simulations, and the nonlocal parameter is calibrated through the verification process. The simulation results reveal that the calibrated nonlocal parameter depends on boundary conditions and vibrational modes. The nonlocal plate model is found to be indispensable in vibration analysis of grapheme sheets with a length less than 8 nm on their sides.

A review on nanomechanical resonators and their applications in sensors and molecular transportation

“…They showed that the local plate model overestimates the resonant frequencies of the sheets with a percentage difference up to 62% at sizes of 2.47 nm. 92 Their results showed that the difference between local and nonlocal plate models remains significant in all aspect ratios as presented in Figure 5, and the overestimation is around 50% at aspect ratio of a=b ¼ 4. Therefore, the nonlocal plate model is strictly necessary for the rectangular GSs with a short side.…”

“…Their simulation results show that the magnitudes of the smallscale parameter are 1.41 nm and 0.87 nm for simply supported and clamped graphenes, respectively. Arash and Wang 92 investigated free vibrations of SLGSs and doublelayered GSs (DLGSs) with different boundary conditions using the nonlocal plate model and MD simulations. They showed that the local plate model overestimates the resonant frequencies of the sheets with a percentage difference up to 62% at sizes of 2.47 nm.…”

“…However, the review is only restricted to classical MD simulations of CNT, GS, and nanowire resonators. 14,16,17,[24][25][26]29,43,45,47,91,92,[137][138][139][140][141][142][143][144] Duan et al 143 investigated the free vibration of singlewalled CNTs (SWCNTs) using MD simulations and the nonlocal Timoshenko beam model. They investigated the effect of boundary conditions and the length-to-diameter aspect ratio of nanotubes on their resonant frequencies.…”

“…The histories of the geometric center of free atoms are recorded for a certain duration depending on the size and the boundary conditions of the GS, and then the vibration frequencies are computed using the fast Fourier transform method. 91,92 Molecular simulations are also employed to study dynamic behavior of nanowires.…”

Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

“…Bending, vibration, and buckling of rectangular and circular GSs have been studied by different researchers [24][25][26][27][28][29][30][31][32][33][34]. For example, Arash and Wang [35] investigated the vibration of single-and doublelayered graphene sheets (SLGSs and DLGSs) using the nonlocal elasticity theory and molecular dynamics simulations. The nonlocal parameter was calibrated through the verification of natural frequency obtained by the nonlocal elasticity theory and molecular dynamics simulations.…”