scholarly journals Modeling of van der Waals force for infinitesimal deformation of multi-walled carbon nanotubes treated as cylindrical shells

2005 ◽  
Vol 42 (23) ◽  
pp. 6032-6047 ◽  
Author(s):  
Xiao Qiao He ◽  
Sritawat Kitipornchai ◽  
C.M. Wang ◽  
K.M. Liew
Keyword(s):  
Carbon Nanotubes ◽  
Cylindrical Shells ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Infinitesimal Deformation ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Finite Element Modeling of van der Waals Interaction for Elastic Stability of Multi-Walled Carbon Nanotubes

2008 ◽  
Vol 55-57 ◽  
pp. 525-528 ◽  
Author(s):  
Chawis Thongyothee ◽  
Somchai Chucheepsakul
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Van Der Waals ◽  
Compressive Force ◽  
Covalent Bond ◽  
Van Der Waals Force ◽  
Tube Length ◽  
Axial Compressive Force ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

The purpose of this study is to assess the effect of van der Waals interactions within multi-walled carbon nanotubes with the three dimensional finite element models. The elastic buckling behaviors of nanotubes are treated under axial compressive force acting on open both ends of nanotubes and considered with various boundary conditions. The analysis is based on the assumptions that the covalent bond of each wall is represented by an elastic beam element while the van der Waals force of adjacent walls are represented by a nonlinear truss element following the Lennard-Jones “6-12” theory. The models of double-walled carbon nanotubes are used to explain the characteristic of multi-walled carbon nanotubes and then results compared with the column theory. The results show that the critical load of nanotubes depends on atomic arrangement, tube length, and number of walls, while the van der Waals force has a small effect on the buckling load for multi-walled carbon nanotubes.

Effect of van der Waals force on wave propagation in viscoelastic double-walled carbon nanotubes

2018 ◽  
Vol 32 (24) ◽  
pp. 1850291
Author(s):  
Yugang Tang ◽  
Ying Liu
Keyword(s):  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Strain Gradient Theory ◽  
Flexural Wave ◽  
Gradient Theory ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the influence of van der Waals force on the wave propagation in viscoelastic double-walled carbon nanotubes (DWCNTs) is investigated. The governing equations of wave motion are derived based on the nonlocal strain gradient theory and double-walled Timoshenko beam model. The effects of viscosity, van der Waals force, as well as size effects on the wave propagation in DWCNTs are clarified. The results show that effects of van der Waals force on waves in inner and outer layers of DWCNTs are different. Flexural wave (FW) in outer layer and shear wave (SW) in inner layer are sensitive to van der Waals force, and display new phenomena. This new finding may provide some useful guidance in the acoustic design of nanostructures with DWCNTs as basic elements.

Vibration Simulations of Double-Walled Carbon Nanotubes by Finite Element Method

2013 ◽  
Vol 774-776 ◽  
pp. 21-24
Author(s):  
Yu Jia ◽  
Li Jie Chen ◽  
Qi Zhao
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Natural Frequency ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Vacancy Defects ◽  
Vibration Behavior ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Finite element (FE) method is used to study the vibration behavior of armchair and zigzag double-walled carbon nanotubes (DWCNTs). In the analysis, nonlinear spring elements and the Lennard-Jones potential function are used to simulate the Van der Waals' force between non-bond atoms of different tube layers. We systematically analyze the effects of aspect ratio, double-atom vacancy defects and Van der Waals' force on the vibration behavior of DWCNTs. The simulation results show that the first order natural frequency decreases with the increase of length-to-diameter ratio (aspect ratio), the existence of Van der Waals' force causes the increase of natural frequency, and double-atom vacancy defects results in the decrease of each order natural frequency.

Comparison of Frequency Response of Parametric Resonance of DWCNT and SWCNT Under Electrostatic Actuation

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Frequency Response ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Beam Model ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated ◽  
Walled Carbon Nanotubes

Abstract This paper deals with electrostatically actuated Double-Walled Carbon Nanotubes (DWCNT) and Single-Walled Carbon Nanotubes (SWCNT) cantilever resonators. Frequency response of parametric resonance is investigated. Euler-Bernoulli cantilever beam model is used for both DWCNT and SWCNT. Electrostatic and viscous damping forces are applied on both types of resonators, DWCNT and SWCNT. In this investigation, soft AC voltage excitation is assumed. For the DWCNT, an intertube van der Waals force is present between the two concentric carbon nanotubes (CNTs), coupling their motion and acting as a nonlinear spring. The nonlinearities in the vibration are provided by the electrostatic (both SWCNT and DWCNT) and intertube van der Waals forces (DWCNT). The Method of Multiple Scales (MMS) is a perturbation method that provides uniformly valid approximations for weakly nonlinear systems. A Reduced-Order-Model (ROM) is developed and numerically solved using AUTO-07P (bifurcation and continuation software). Since large tip deflections are investigated in this paper, only coaxial vibration of the DWCNT is considered. Parametric resonance is investigated, as well as the influences of damping and voltage. Lastly, the effect of intertube van der Waals force on the bifurcation and stability of the DWCNT is reported.

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