Modal analysis of carbon nanotubes and nanocones using FEM

Vibration and Elastic Buckling Analyses of Single-Walled Carbon Nanocones

“…When free-clamped and clamped-clamped boundary conditions are considered, the first fundamental frequencies of SWCNCs, are found to be in the range of 0.36 -2.52 THz. Lee and Lee [28] used Timoshenko beam element formulations which include shear deformation effects but they employed Euler-Bernoulli beam element constants (i.e., see Table 1) [23]; this assumption affects the natural frequencies of SWCNC that are found to be lower than those of Euler-Bernoulli beam elements. In addition, density of beam elements is selected to be the density of GSs (i.e.…”

“…Both of the models in Li and Chou [19] and Scarpa and Adhikari [34] yield the same deformation results as the structural mechanics stiffness constants in the AMBER force model are equal [33] if the corresponding element properties are used given in Table 1. Lee and Lee [28] used Timoshenko beam element formulations which include shear deformation effects but they employed Euler-Bernoulli beam element constants (i.e., see Table 1) [23]; this assumption affects the natural frequencies of SWCNC that are found to be lower than those of Euler-Bernoulli beam elements. If shear deformation effects are considered, parameters of shear beam formulations given in Scarpa and Adhikari [34,35] should be used.…”

“…In addition, Lee and Lee [28] studied of vibrations of SWCNCs; however, they did not examine the effects of cone height and used Timoshenko beam formulations with Euler-Bernoulli beam parameters which may lead to lower modal frequencies than actual values. Motivated by these facts, vibration and elastic buckling analysis of SWCNCs are completed by using the MM based FE approach [19,23] where Euler-Bernoulli beam elements with consistent mass matrix are used.…”

“…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.…”

“…Experimental measurements for prediction of the mechanical properties of CNCs are very difficult and costly. Thus, computational tools are widely used to characterize mechanical properties of CNCs [6,7,[14][15][16][17]28]. Kumar et al [6] investigated the Young's and shear modulus of CNCs employing second-generation reactive empirical bond-order potential.…”