Vibrational analysis of single-layered graphene sheets

Abstract

A molecular structural mechanics method has been implemented to investigate the vibrational behavior of single-layered graphene sheets. By adopting this approach, mode shapes and natural frequencies are obtained. Vibrational analysis is performed with different chirality and boundary conditions. Numerical results from the atomistic modeling are employed to develop predictive equations via a statistical nonlinear regression model. With the proposed equations, fundamental frequencies of single-layered graphene sheets with considered boundary conditions can be predicted within 3% difference with respect to the atomistic simulation.

Vibration and Elastic Buckling Analyses of Singlewalled Carbon Nanocones

“…Hence, natural frequencies of SWCNCs are found to be less than 100GHz in all calculations for the same type of SWCNCs having the height of 20 Ǻ and with free-clamped and clamped-clamped boundary conditions. These frequency ranges are comparable with those of CNTs and SLGSs (i.e., 10 GHz -1.5 THz for SWCNTs and 2.4 GHz -3.5 THz for SLGSs) which are reported in literature [21,25].…”

“…Tserpes and Papanikos [23] introduced an atomistic FE method based on the approach of Li and Chou [19] to model CNTs by using commercial FE codes; they identified the C-C bond thickness d, Young's modulus E and shear modulus G by using the AMBER force model [19]. By using the methods developed by Li and Chou [19] and Tserpes and Papanikos [23]; Hashemnia et al [24] and Sakhaee-Pour et al [25] examined natural frequencies and mode shapes of single-layered graphene sheets (SLGSs) and Sakhaee-Pour et al [25] predicted fundamental frequencies of SLGSs with equivalent lengths that are found to be in the range of 2.4 GHz -3.5 THz; Sakhaee-Pour et al [26] studied natural frequencies and mode shapes SWCNTs; Sakhaee-Pour [27] analyzed elastic buckling of SLGSs; Lee and Lee [28] studied vibrational behaviors of SWCNTs and SWCNCs, and predicted fundamental frequencies of SWCNCs below 20 GHz with a cone having the height of 20 Ǻ; Mir et al [29] studied natural frequencies and mode shapes of SWCNTs; Cheng et al [30] and Fan et al [31] examined mechanical properties of CNTs such as Young's modulus, shear modulus, natural frequency and buckling load; Avila et al [32] analyzed elastic and vibrational properties of GSs and CNTs; we studied twoand three-dimensional modal and transient analyses of SLGSs in [33]. In the works [19 -27, 29, 30-33], Euler-Bernoulli beam elements are used to represent bond interactions between C-C atoms in GSs, CNTs and CNCs.…”

Transverse vibration of single-layer graphene sheets

“…The main novelty of our paper is the MM [36,37], which is a higher fidelity model compared with the previously used models [20,38] where the SM approach is used. In the MM approach, the molecule first finds the lowest energy configuration from its pre-optimized state and then the a b Figure 1.…”

“…Planar structure such as SLGS may deform to attain the lowest energy configuration. This is ignored in the SM approach [20,38], which only considers the initial geometry of the molecule. In the SM approach the Euler-Bernoulli beam model is used to represent the C-C bonds and subsequently the finite element method [39] is used to discretize the equation of motion and obtain the natural frequencies.…”

Scale effects on ultrasonic wave dispersion characteristics of monolayer graphene embedded in an elastic medium

“…In addition, it should be mentioned that graphite is composed of multilayered sheets, but it was recently reported [Horiuchi et al 2004] that single-layered sheets are detectable in carbon nanofilms. Sakhaee-Pour et al [2008a] have studied the free vibrational behavior of single-layer graphene sheets (SLGS) while considering the effects of chirality and aspect ratio as well as boundary conditions, and have developed predictive models for computing the natural frequencies. The potential applications of SLGSs as mass sensors and atomistic dust detectors have further been investigated [Sakhaee-Pour et al 2008b].…”