Variational Principles for Vibrating Carbon Nanotubes Modeled as Cylindrical Shells Based on Strain Gradient Nonlocal Theory

2011 ◽  
Vol 8 (10) ◽  
pp. 1954-1962 ◽  
Author(s):  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Strain Gradient ◽  
Variational Principles ◽  
Cylindrical Shells ◽  
Nonlocal Theory

scholarly journals Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 87
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Scale Effects ◽  
Nonlocal Theory ◽  
Elastic Plates ◽  
Critical Temperatures ◽  
Buckling Behavior ◽  
Linear Vibrations ◽  
Nonlocal Strain Gradient ◽  
Plate Kinematics

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

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.

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

scholarly journals Variational Principles for Multiwalled Carbon Nanotubes Undergoing Vibrations Based on Nonlocal Timoshenko Beam Theory

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Ismail Kucuk ◽  
Ibrahim S. Sadek ◽  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Multiwalled Carbon Nanotubes ◽  
Timoshenko Beam ◽  
Variational Principles ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Small Scale ◽  
Multiwalled Carbon ◽  
Nonlocal Timoshenko Beam Theory

Variational principles are derived for multiwalled carbon nanotubes undergoing linear vibrations using the semi-inverse method with the governing equations based on nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. Physical models based on the nonlocal theory approximate the nanoscale phenomenon more accurately than the local theories by taking small scale phenomenon into account. Variational formulation is used to derive the natural and geometric boundary conditions which give a set of coupled boundary conditions in the case of free boundaries which become uncoupled in the case of the local theory. Hamilton's principle applicable to this case is also given.

Variational Principles for the Stability Analysis of Multi-Walled Carbon Nanotubes Based on a Nonlocal Elastic Shell Model

2010 ◽  
Author(s):  
Mohsen Asghari ◽  
Jacob Rafati
Keyword(s):  
Carbon Nanotubes ◽  
Stability Analysis ◽  
Inverse Method ◽  
Variational Principles ◽  
Elastic Shell ◽  
Multi Walled Carbon Nanotubes ◽  
Natural Boundary Conditions ◽  
The Stability ◽  
Walled Carbon Nanotubes ◽  
Continuum Theories

The nonlocal continuum theories are capable to reflect the small length characteristic of nanostructures. In this work, variational principles are presented for the stability analysis of multi-walled carbon nanotubes under various mechanical loadings based on the nonlocal elastic Donnell’s shell by the semi-inverse method. In this manner, a set of proper essential and natural boundary conditions for each layer of the multi-walled nanotube is derived.

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