Torsional Vibration Analysis of Carbon Nanotubes Based on the Strain Gradient Theory and Molecular Dynamic Simulations

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
S. Ajori
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Molecular Dynamic ◽  
Strain Gradient ◽  
Torsional Vibration ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Molecular Dynamic Simulations ◽  
Dynamic Simulations

In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.

Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory

2019 ◽  
Vol 26 (5-6) ◽  
pp. 277-305
Author(s):  
Hosein Shahraki ◽  
Hossein Tajmir Riahi ◽  
Mohsen Izadinia ◽  
Sayed Behzad Talaeitaba
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Vibration Analysis ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Reinforced Composite ◽  
Nonlocal Strain Gradient

This paper investigates the buckling and free vibration analysis of functionally graded carbon nanotube-reinforced composite thick rectangular nanoplates resting on a Kerr foundation under different boundary conditions. Quasi-three-dimensional hyperbolic shear deformation theory is employed to study the effects of transverse shear deformation and thickness stretching. To capture the small-size effects of nanoscale dimensions, the nonlocal strain gradient theory is used, which includes nonlocal parameters and length scale of the material. In this study, rectangular nanocomposite plates are reinforced by carbon nanotubes which are assumed to be graded through the thickness direction with four types of distributions, namely, uniformly, FG-O, FG-V, and FG-X. The governing equations and boundary conditions are extracted within Hamilton’s principle. They are discretized and numerically solved by utilizing a generalized differential quadrature method. The critical buckling loads and natural frequencies are determined by solving the eigenvalue problem. The accuracy of present results is validated with those available in the literature. Also, the effect of various factors, such as aspect ratio, length-to-thickness ratio, in-plane loading factor, length scale parameter, nonlocal parameter, volume fraction and dispersion profile of carbon nanotubes, elastic foundation coefficients, and different boundary conditions, on the buckling behavior and free vibration of nanoplates is investigated.

scholarly journals Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes

2019 ◽  
Vol 9 (3) ◽  
pp. 514 ◽  
Author(s):  
Raffaele Barretta ◽  
Marko Čanadija ◽  
Francesco Marotti de Sciarra
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Scale Effects ◽  
Nonlocal Problem ◽  
Gradient Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nano Rods ◽  
Nonlocal Strain Gradient

Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the extensional behavior of nano-rods. The considered integral elasticity model, involving axial force and strain fields, is conveniently shown to be equivalent to a nonlocal differential problem equipped with constitutive boundary conditions. Unlike treatments in the literature, no higher-order boundary conditions are required to close the nonlocal problem. Closed-form solutions of elastic nano-rods under selected loadings and kinematic boundary conditions are provided. As an innovative implication, Young’s moduli of Single-Walled Carbon Nanotubes (SWCNT) weare assessed and compared with predictions of Molecular Dynamics (MD). New benchmarks for numerical analyses were also detected.

scholarly journals Flow of long chain hydrocarbons through carbon nanotubes (CNTs)

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pranay Asai ◽  
Palash Panja ◽  
Raul Velasco ◽  
Milind Deo
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamic ◽  
Continuum Models ◽  
Molecular Dynamic Simulations ◽  
Dynamic Simulations ◽  
Pharmaceutical Applications ◽  
Molecular Sizes ◽  
Hydrocarbon Molecules ◽  
Pressure Driven Flow ◽  
Long Chain

AbstractThe pressure-driven flow of long-chain hydrocarbons in nanosized pores is important in energy, environmental, biological, and pharmaceutical applications. This paper examines the flow of hexane, heptane, and decane in carbon nanotubes (CNTs) of pore diameters 1–8 nm using molecular dynamic simulations. Enhancement of water flow in CNTs in comparison to rates predicted by continuum models has been well established in the literature. Our work was intended to observe if molecular dynamic simulations of hydrocarbon flow in CNTs produced similar enhancements. We used the OPLS-AA force field to simulate the hydrocarbons and the CNTs. Our simulations predicted the bulk densities of the hydrocarbons to be within 3% of the literature values. Molecular sizes and shapes of the hydrocarbon molecules compared to the pore size create interesting density patterns for smaller sized CNTs. We observed moderate flow enhancements for all the hydrocarbons (1–100) flowing through small-sized CNTs. For very small CNTs the larger hydrocarbons were forced to flow in a cork-screw fashion. As a result of this flow orientation, the larger molecules flowed as effectively (similar enhancements) as the smaller hydrocarbons.

Free nonlinear vibration analysis of nano-truncated conical shells based on modified strain gradient theory

2021 ◽  
pp. 146442072110419
Author(s):  
Alireza Sheykhi ◽  
Shahrokh Hosseini-Hashemi ◽  
Adel Maghsoudpour ◽  
Shahram E Haghighi
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Couple Stress ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Conical Shells ◽  
Modified Couple Stress

In this study, the nonlinear free vibrations behaviour of nano-truncated conical shells was analysed, using the first-order shear deformable shell model. The analysis took into account the structure size through modified strain gradient theory, and differential quadrature and Fréchet derivative methods in von Kármán-Donnell-type approach to kinematic nonlinearity. The governing equations were obtained, utilizing Hamilton's principle. Partial differential equations plus the non-classical and classical boundary conditions were used to obtain the shells’ equations of motion. Discretizing the boundary conditions and equations of motion were performed based on a generalized differential quadrature analogy. The eigenvalue system was considered based on the harmonic balance technique. The Galerkin and Fréchet derivative approaches were used to determine the nonlinear free vibration behaviour of the carbon nano-cone, which was modelled in the simply- and clamped-supported boundary conditions. Comparisons were made between the findings from the new model versus the couple and classical stress theories, indicating that the classical and modified couple stress theories are distinct representations of modified strain gradient theory. The results also revealed that the degree of hardening of nano-truncated conical shells in the modified strain gradient theory is less than that of modified couple stress and classical theories. This led to a rise in the non-dimensional amplitude and frequency ratios. This study investigated the effect of size on free nonlinear vibrations of nano-truncated conical shells for various apex angles and lengths. Finally, we evaluated and compared our findings versus those reported by previous studies, which confirmed the precision and accuracy of our results.

A nonlocal strain gradient theory for rotating thermo-mechanical characteristics on magnetically actuated viscoelastic functionally graded nanoshell

2020 ◽  
Vol 31 (12) ◽  
pp. 1511-1523
Author(s):  
Mohammad Mahinzare ◽  
Hossein Akhavan ◽  
Majid Ghadiri
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Smart Structure ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Nonlocal Strain Gradient

In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.

Dynamic behaviours of carbon nanotubes under dc voltage based on strain gradient theory

2013 ◽  
Vol 46 (40) ◽  
pp. 405101 ◽  
Author(s):  
Mir Masoud Seyyed Fakhrabadi ◽  
Abbas Rastgoo ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Carbon Nanotubes ◽  
Strain Gradient ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Dc Voltage

Equilibrium equations and boundary conditions of strain gradient theory in arbitrary curvilinear coordinates

2014 ◽  
Vol 23 (5-6) ◽  
pp. 169-176
Author(s):  
Mikhail Guzev ◽  
Chengzhi Qi ◽  
Jiping Bai ◽  
Kairui Li
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Strain Gradient ◽  
Special Form ◽  
Curvilinear Coordinates ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Equilibrium Equations ◽  
Plane Strain Problem

AbstractEquilibrium equations and boundary conditions of the strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric plane strain problem is also given.

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