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.

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.

The Computation of Elastic Constants of Double Wall Carbon Nanotubes Based on the Finite Element Method Considering Van Der Waals' Force

2012 ◽  
Vol 562-564 ◽  
pp. 334-338 ◽  
Author(s):  
Li Jie Chen ◽  
Lin Bo Li ◽  
Qi Zhao
Keyword(s):  
Finite Element Method ◽  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Elastic Constants ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Internal Layer ◽  
The Finite Element Method ◽  
Double Wall

Based on the finite element method (FEM), we study the elastic constants of double-wall carbon nanotubes (DWCNTs). In the models, the Lennard-Jones potential function is used to consider the Van der Waals' force between non-bond atoms from different layers. The variations of the elastic constants with the diameter and the aspect ratio of the internal layer nanotube are investigated systematically. The computational results indicate that for both the armchair and the zigzag DWCNTs, the elastic moduli are generally lower than those of the single-wall carbon nanotubes with the same chirality as the internal and external layers. With the increase of the diameter and the aspect ratio of the internal layer carbon nanotubes, the elastic constant of DWCNTs will fall to a stable value.

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.

Investigation of the Fundamental Frequency of Double Walled Carbon Nanotubes Using Molecular Mechanics Approach by an Averaging Van Der Waals Forces Modeling

2011 ◽  
Author(s):  
Ehsan Asadi ◽  
Ali Karimzade ◽  
Mehrdad Farid
Keyword(s):  
Carbon Nanotubes ◽  
Aspect Ratio ◽  
Molecular Mechanics ◽  
Fundamental Frequency ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Covalent Bonds ◽  
Fundamental Frequencies ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Carbon nanotubes have received a lot of attention since their introduction in 1991 because of novel properties that show substantial promises for use in many applications. Their usage depends on the strength of our knowledge of their properties. In this work, molecular mechanics approach is used to study the mechanical properties of multi-wall carbon nanotubes. In particular this paper investigates fundamental frequency of double walled carbon nanotubes. Carbon nanotubes are big and long molecules that can be regarded as mechanical structures. In modeling of multi-walled carbon nanotubes, two distinct atomic bonds are required to be modeled, i.e. covalent bonds between the neighboring carbon atoms in the same layer and Van der Waals bonds between close atoms in neighboring layers. In this approach, for modeling of each wall; covalent bonds are modeled by beam joints such that atoms are considered to be concentrated masses at the ends. Interactions of neighboring walls that are mainly due to Van der Waals forces are treated to be truss rods in modeling. The most challenging aspect of modeling is to define truss rod properties as they are highly nonlinear. We utilized an averaging method for finding truss rod properties. Finite Element Method is employed to obtain Fundamental frequencies. Results are compared to available researches and a close agreement is observed. Results indicate that by increasing aspect ratio, fundamental frequency of double walled nanotubes decrease. In addition, double walled carbon nanotubes have higher fundamental frequencies at clamp-clamp in comparison to clamp-free condition; however, this difference becomes negligible as aspect ratio increases.

Axial Buckling Behavior of Double-Wall Carbon Nanotubes by Finite Element Simulation

2012 ◽  
Vol 562-564 ◽  
pp. 339-342
Author(s):  
Li Jie Chen ◽  
Yi Fan Zhang ◽  
Qi Zhao
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Van Der Waals ◽  
Maximum Amplitude ◽  
Van Der Waals Force ◽  
Single Wall Carbon Nanotubes ◽  
Buckling Behavior ◽  
Element Simulation ◽  
Double Wall

With finite element (FE) simulation, we study the buckling behavior of double-wall carbon nanotubes (DWCNTs) under axial compression. In the FE models, linear beam elements and nonlinear spring elements are used to simulate the complex structures and the Van der Waals' force between non-bond atoms from different layers is considered by the Lennard-Jones potential function. The effect of aspect ratio of DWCNTs and double-atoms vacancy on the buckling modes and the critical buckling strains are investigated. The computational results indicate that with the increase of aspect ratio, the critical buckling strains will decrease. For both armchair and zigzag DWCNTs, the critical buckling strains are generally larger than those of the single-wall carbon nanotubes with the same chirality as the external layers and those of the same structures without Van der Waals' force. For defective DWCNTs, the buckling strains of each order decrease by a maximum amplitude of 32.3%.

Comparison of Frequency Response of Primary Resonance of DWCNT and CNT Resonators Under Electrostatic Actuation

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Electrostatic Actuation ◽  
Amplitude Response ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Abstract This paper deals with the frequency-amplitude response of primary resonance of electrostatically actuated Double-Walled Carbon Nanotubes (DWCNT) and Single-Walled Carbon Nanotubes (SWCNT) cantilever resonators. Their responses are compared. Both the DWCNT and SWCNT are modeled as Euler-Bernoulli cantilever beams. Electrostatic and damping forces are applied on both types of resonators. An AC voltage provides a soft electrostatic actuation. For the DWCNT, intertube van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes and acting as a nonlinear spring between the two carbon nanotubes. Electrostatic (for SWCNT and DWCNT) and intertube van der Waals (for DWCNT) forces are nonlinear. Both resonators undergo nonlinear parametric excitation. The Method of Multiple Scales (MMS) is used to investigate the systems under soft excitations and weak nonlinearities. A 2-Term Reduced-Order-Model (ROM) is numerically solved for stability analysis using AUTO-07P, a continuation and bifurcation software. The coaxial vibrations of DWCNT are considered in this work, in order to draw comparisons between DWCNT and SWCNT. Effects of damping and voltage of the frequency-amplitude response are reported.

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