Dynamical Stability Behaviors of Fluid-Conveyed Double-Walled Carbon Nanotubes

2011 ◽  
Vol 268-270 ◽  
pp. 138-142
Author(s):  
Yan Yan ◽  
Wen Quan Wang
Keyword(s):  
Carbon Nanotubes ◽  
Flow Velocity ◽  
Critical Role ◽  
Elastic Beam ◽  
Model Potential ◽  
Dynamical Stability ◽  
Beam Model ◽  
Time Histories ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Based on an elastic beam model, potential flow theory and N-mode Galerkin discretization technique, the dynamical stability behaviors of fluid-conveyed double-walled carbon nanotubes (DWCNTs) considering geometry nonlinearity relating to the time as variation of the flow velocity are studied. The results show that the bifurcations happen in turn of pitchfork and Hopf types as the flow velocity increases. The vdW forces do not change the bifurcation types but make the critical velocities increase sharply. Furthermore, the vdW forces play a critical role in keeping the synchronization of the time histories of the amplitudes or the velocities of different layers of the CNTs-fluid system.

EFFECT OF THE VAN DER WAALS INTERACTION ON ANALYSIS OF DOUBLE-WALLED CARBON NANOTUBES

2005 ◽  
Vol 05 (03) ◽  
pp. 457-474 ◽  
Author(s):  
Q. WANG
Keyword(s):  
Carbon Nanotubes ◽  
Van Der Waals ◽  
Elastic Beam ◽  
Beam Model ◽  
Mechanical Models ◽  
Parametric Studies ◽  
Kink Instability ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Vdw Interaction

This paper presents the research on the analysis of the van der Waals (vdW) interaction on double-walled carbon nanotubes (DWNTs) via an elastic beam model. The parametric studies on the size of DWNTs are conducted to show the effect of vdW interaction on the analysis of both a cantilever DWNT subjected to force at the free tip and a DWNT subjected to pure bending. In addition, the kink instability for the cantilever DWNT is analyzed based on the proposed beam model. It is hoped that the research will provide mechanical models for the analysis of both single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs), as well as for kink instability analysis of carbon nanotubes (CNTs).

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.

Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model

2015 ◽  
Vol 5 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Variational Principles ◽  
Linear Time ◽  
Scale Effects ◽  
Time Dependent ◽  
Small Scale ◽  
Beam Model ◽  
Geometric Boundary ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractVariational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

Vibration of Cantilevered Double-Walled Carbon Nanotubes Predicted by Timoshenko Beam Model and Molecular Dynamics

2015 ◽  
Vol 12 (04) ◽  
pp. 1540017 ◽  
Author(s):  
Rumeng Liu ◽  
Lifeng Wang
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Natural Frequencies ◽  
Md Simulations ◽  
Beam Model ◽  
Timoshenko Beams ◽  
Fundamental Frequencies ◽  
The Difference ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Vibration of double-walled carbon nanotubes (DWCNTs) with one end fixed and the other end free is studied by using different beam models of continuum mechanics and the molecular dynamics (MD) simulations. The models of the double-Euler beams (DEB) and the double-Timoshenko beams (DTB) of cantilevered case, with the van der Waals interaction between layers taken into consideration, are applied to predict the natural frequencies of DWCNTs. An analytical solution is first obtained for the DTB model with cantilevered boundary condition. The fundamental frequencies obtained by the DEB model and the DTB model are very close, for the relatively long DWCNTs. The MD simulations show that these two models can predict the natural frequencies well. However, the difference between the DEB model and the DTB model becomes obvious, for the vibration of the relatively short DWCNTs. The DTB model can offer a much better prediction than the DEB model when the DWCNT is very short especially for high-order frequencies.

scholarly journals Influence of the nonlocal parameter on the transverse vibration of double-walled carbon nanotubes

2015 ◽  
Vol 24 (3-4) ◽  
pp. 79-90
Author(s):  
Fernanda de Borbón ◽  
Daniel Ambrosini
Keyword(s):  
Carbon Nanotubes ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Elastic Stiffness ◽  
Beam Model ◽  
Transverse Vibrations ◽  
Proposed Model ◽  
Cubic Polynomials ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractA high-order nonlocal continuum beam model is proposed, which can be applied to study the transverse vibrations of double-walled carbon nanotubes (DWCNTs), including those that could have initial deformations due to defects or external actions. A beam element is developed adopting Hermite cubic polynomials as shape functions, and mass and elastic stiffness matrix are presented. The influence of the nonlocal parameter on the vibrational properties of DWCNTs is studied. Using the proposed model, it was found that the nonlocal parameter has a strong influence on the natural frequencies.

Nonlocal Flügge Shell Model for Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
R. Ansari ◽  
B. Arash
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Shell Model ◽  
Scale Effects ◽  
Elastic Shell ◽  
Small Scale ◽  
Geometrical Parameters ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the vibrational behavior of double-walled carbon nanotubes (DWCNTs) is studied by a nonlocal elastic shell model. The nonlocal continuum model accounting for the small scale effects encompasses its classical continuum counterpart as a particular case. Based upon the constitutive equations of nonlocal elasticity, the displacement field equations coupled by van der Waals forces are derived. The set of governing equations of motion are then numerically solved by a novel method emerged from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions. The influences of small scale factor, layerwise boundary conditions and geometrical parameters on the mechanical behavior of DWCNTs are fully investigated. Explicit expressions for the nonlocal frequencies of DWCNTs with all edges simply supported are also analytically obtained by a nonlocal elastic beam model. Some new intertube resonant frequencies and the corresponding noncoaxial vibrational modes are identified due to incorporating circumferential modes into the shell model. A shift in noncoaxial mode numbers, not predictable by the beam model, is also observed when the radius of DWCNTs is varied. The results generated also provide valuable information concerning the applicability of the beam model and new noncoaxial modes affecting the physical properties of nested nanotubes.

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