Vibrational analysis of single-walled carbon nanocones using molecular mechanics approach

Fakhrabadi, Mir Masoud Seyyed; Khani, Navid; Pedrammehr, Siamak

doi:10.1016/j.physe.2012.01.004

Cited by 29 publications

(5 citation statements)

References 14 publications

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“…Using equations (32) and substituting equations ( 25)-( 30) into equations. ( 19)-( 24), the normalized nonlinear motion equations can be obtained which could not be solved analytically.…”

Section: Energy Methodsmentioning

confidence: 99%

“…The buckling behavior of the CNCs using the same simulation as 30 is investigated by Tsai and Fang. 31 Fakhrabadi et al 32,33 studied vibrational, elastic and buckling behaviors of CNCs with different lengths and apex angles in various boundary conditions using the MD-based finite element method (FEM). Based on the continuum Lennard-Jones model, Ansari et al 34 investigated the vdWs interaction of two concentric and eccentric CNCs with different or identical sizes.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Arani

Kolahchi

2013

Proceedings of the Institution of Mechanical Engineers, Part C:

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Nonlinear vibration and instability of embedded double-walled carbon nanocones subjected to axial load are investigated in this article based on Eringen's nonlocal theory and Timoshenko beam model. The elastic medium is simulated as Pasternak foundation and the van der Waals forces between the inner and the outer layers of double-walled carbon nanocones are taken into account. Using von Kármán geometric nonlinearity, energy method and Hamilton’s principle, the nonlocal nonlinear motion equations are obtained. The differential quadrature method is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency and critical fluid velocity of viscous-fluid-conveying double-walled carbon nanocones. A detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, thickness-to-length ratio, temperature change, apex angles, elastic medium and van der Waals forces on the dimensionless frequency and critical buckling load of double-walled carbon nanocones. The results show that the small-size effect on the nonlinear frequency is significant and cannot be neglected; also, the nonlinear frequency and critical buckling load decrease with increasing the cone apex-angle.

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“…Using equations (32) and substituting equations ( 25)-( 30) into equations. ( 19)-( 24), the normalized nonlinear motion equations can be obtained which could not be solved analytically.…”

Section: Energy Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Arani

Kolahchi

2013

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Singh and Patel [50] also studied the nonlinear elastic response of SLGSs and reported that SLGSs show softening behavior at small strains and hardening behavior at large bending. Fakhrabadi et al [45] studied the vibrational properties of CNCs of different heights and cone angles using MM simulations and reported that the transverse vibrational frequencies reduce with increase in cone angle and height. Hu et al [46] modelled CNCs as tapered beams using the Euler-Bernoulli and Timoshenko beam theory to study transverse vibrations.…”

Section: Introductionmentioning

confidence: 99%

Comparing quantum, molecular and continuum models for graphene at large deformations

Mokhalingam

Ghaffari

Sauer

et al. 2020

Carbon

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In this paper, the validity and accuracy of three interatomic potentials, commonly used to study carbon nanostructures in molecular dynamics, and the continuum shell model of Ghaffari and Sauer [1] are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) near zero Kelvin is studied for this comparison. The validity of the molecular and continuum models is assessed by direct comparison with density functional theory (DFT) data available in the literature. The molecular simulations are carried out employing the MM3, Tersoff and REBO+LJ potentials. The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements. For the comparison, the nonlinear response of a square graphene sheet under uniaxial stretching, biaxial stretching and pure bending is studied. Results from the continuum model are in good agreement with those of DFT. The results from the MM3 potential agree well with the DFT results up to the instability point, whereas those from the REBO+LJ and Tersoff potentials agree with the DFT results only within the range of small deformations. In contrast to the other potentials, the Tersoff potential yields auxetic response in SLGSs under uniaxial stretch. Additionally, the transverse vibration frequencies of a pre-stretched graphene sheet and a carbon nanocone are obtained using the continuum model and molecular simulations with the MM3 potential. The variations of the frequencies obtained from these two approaches agree within an accuracy of about 95\%.

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“…Specifically, they have presented many of the related theoretical research efforts, which involve continuum, atomistic, and hybrid atomistic/continuum models on this field. Molecular mechanics (MM) methods have been in the forefront of the research on studying the mechanical properties [2,3] as well as vibrational response [4][5][6] of nanomaterials. This is due to the fact that MM methods have some distinct advances in comparison with other theoretical techniques such as molecular dynamics (MD), quantum mechanics (QM), and continuum mechanics (CM) methods.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Atom Vacancy Defect on the Vibrational Behavior of Single-Walled Carbon Nanotubes: A Structural Mechanics Approach

Georgantzinos

Giannopoulos

Anifantis

2014

Advances in Mechanical Engineering

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An atomistic structural mechanics method, which is based on the exclusive use of spring elements, is developed in order to study the effect of imperfections due to atom vacancy on the vibrational characteristics of single-walled carbon nanotubes (SWCNTs). The developed elements simulate the relative translations and rotations between atoms as well as the mass of the atoms. In this way, molecular mechanics theory can be applied directly because the atomic bonds are modeled by using exclusively physical variables such as bond stretching. The method is validated for its predictability comparing with vibration results found in the open literature for pristine nanotubes. Then, it is used for the vibration analysis of defective nanotubes. Imperfections such as one-atom vacancy, two-atom vacancy, and one carbon hexagonal cell vacancy are investigated. Their effect on vibrational behavior is explored for different defect positions, nanotube diameters, and support conditions. According to the obtained results, the fundamental frequency is decreased as the size of imperfection increases, and the percentage reduction in fundamental frequency due to the atomic vacancy defect is more affected for a single-clamped SWCNT than for a double-clamped one.

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Vibrational analysis of single-walled carbon nanocones using molecular mechanics approach

Cited by 29 publications

References 14 publications

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Nonlinear vibration and instability of embedded double-walled carbon nanocones based on nonlocal Timoshenko beam theory

Comparing quantum, molecular and continuum models for graphene at large deformations

The Effect of Atom Vacancy Defect on the Vibrational Behavior of Single-Walled Carbon Nanotubes: A Structural Mechanics Approach

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