Nanoscale finite element models for vibrations of single-walled carbon nanotubes: atomistic versus continuum

Ansari, R.; Rouhi, S.; Aryayi, M.

doi:10.1007/s10483-013-1738-6

Cited by 24 publications

(5 citation statements)

References 30 publications

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“…Ru et al [16] used multipleelastic-shell model to study the vibrations of multiwall carbon nanotubes employing Flugge's equations. Ansari et al [17] used the shell elements in a hybrid approach to model single walled carbon nanotubes and compared it atomistic method. Ghorbanpour Arani et al [18] used Donnel shell model to measure the transverse displacements of single and double-walled carbon nanotubes, the results of which are compared with Euler-Bernoulli and Timoshenko beam models.…”

Section: Literature Reviewmentioning

confidence: 99%

An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

Khan¹

2021

Preprint

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Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

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Section: Literature Reviewmentioning

confidence: 99%

An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

Khan¹

2021

Preprint

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“…Besides, as the atomic methods such as density functional theory (DFT) and molecular dynamics (MD) simulations are time-consuming, the continuum mechanics approaches like FE method are of great importance. [10][11][12][14][15][16][17][18][19] The accuracy of the applied FE method has been proved previously. 16 A three-dimensional finite element model is used to investigate the vibrational behavior of SiC nanostructures in which Si-C bonds are simulated by beam elements.…”

Section: Atomistic Finite Element Modelingmentioning

confidence: 99%

Vibrational analysis of single-layered silicon carbide nanosheets and single-walled silicon carbide nanotubes using nanoscale finite element method

Ansari

Rouhi

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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A three-dimensional finite element model has been used here to study the vibrational behavior of silicon carbide nanosheets and nanotubes. The bonds of hexagonal lattices of SiC nanosheets have been modeled by structural beam elements, and at the corners, mass elements are placed instead of Si and C atoms. Moreover, molecular dynamics simulations are performed to verify the finite element model. Comparing the results of finite element model and molecular dynamics simulations, it is concluded that the utilized approach can predict the results of molecular dynamics simulations with a reasonable accuracy. It is observed that the atomic structure does not significantly affect the vibrational behavior of nanosheets. Besides, increasing the size of nanosheet results in decreasing the effect of geometry variation. As the aspect ratio of nanotubes increases, the effects of boundary conditions and length diminish so that the frequency envelopes tend to converge.

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“…Carbon nanotubes (CNTs) have attracted a lot of attention among researchers due to their extraordinary mechanical, electrical and thermal properties. [1][2][3][4][5][6][7][8][9] Strozzi et al [7][8][9] investigated the linear and nonlinear vibrations of various CNT types. They studied the shell dynamics in the framework of the Sanders-Koiter theory and described the shell deformation in terms of longitudinal, tangential and radial displacement fields.…”

Section: Introductionmentioning

confidence: 99%

Impact resistance of short carbon fibre-carbon nanotube-polymer matrix hybrid composites: A stochastic multiscale approach

Ansari

Ahmadi

Rouhi

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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A multiscale approach is used here to investigate the impact properties of carbon fibre/carbon nanotube-reinforced polymer. For this purpose, the mechanical properties of the carbon nanotubes (CNTs) are obtained by molecular dynamics simulations. Then, they are included in the polyethene matrix, and the mechanical properties of CNT-reinforced polyethene are computed using a stochastic approach. Considering the CNT-reinforced polyethene as the matrix, the effect of adding the carbon fibres on its mechanical properties is investigated in the next step. Finally, utilizing a stochastic method, the macro-scale mechanical properties of carbon fibre/carbon nanotube-reinforced polymer are computed. Thereafter, the impact test is applied on the models. The finite element method is used to investigate the mechanical and impact properties of representative volume elements. The effects of waviness, volume percentage and aspect ratio of the carbon fibre and CNT on the mechanical properties of the multiscale composite are evaluated. It is shown that reinforcing the polyethene matrix by carbon fibres and CNTs significantly increases its impact resistance. Adding 3% and 5% volume percentages of CNT into 3%-carbon fibre/polyethene and 5%-carbon fibre/polyethene respectively, resulted in 26% and 47% improvement in the impact resistance of the composite.

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Nanoscale finite element models for vibrations of single-walled carbon nanotubes: atomistic versus continuum

Cited by 24 publications

References 30 publications

An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

Vibrational analysis of single-layered silicon carbide nanosheets and single-walled silicon carbide nanotubes using nanoscale finite element method

Impact resistance of short carbon fibre-carbon nanotube-polymer matrix hybrid composites: A stochastic multiscale approach

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