Small Scale Effect on Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes with Uncertainty

2013 ◽  
Vol 479-480 ◽  
pp. 121-125
Author(s):  
Tai Ping Chang
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Nonlinear Differential Equations ◽  
Small Scale ◽  
Governing Equations ◽  
Statistical Dynamic ◽  
The Mean ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper investigates the statistical dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. Besides, the small scale effects of the nonlinear vibration of the DWCNTs are studied by using the theory of nonlocal elasticity. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton's principle. The Young's modulus of elasticity of the DWCNTs is assumed as stochastic to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin's method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed; meanwhile the effects of small scale coefficients on the statistical dynamic response of the DWCNTs are investigated.

Stochastic Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes

2013 ◽  
Vol 284-287 ◽  
pp. 362-366
Author(s):  
Tai Ping Chang
Keyword(s):  
Carbon Nanotubes ◽  
Differential Equations ◽  
Nonlinear Vibration ◽  
Nonlinear Differential Equations ◽  
Mean Value ◽  
Stochastic Dynamic ◽  
Governing Equations ◽  
The Mean ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper investigates the stochastic dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton’s principle. The Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to the position to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin’s method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed. It is concluded that the mean value and standard deviation of the amplitude of the displacement increase nonlinearly with the increase of the frequencies.

scholarly journals Buckling analysis of a non-concentric double-walled carbon nanotube

2020 ◽  
Vol 231 (12) ◽  
pp. 5007-5020 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Hamid M. Sedighi
Keyword(s):  
Carbon Nanotubes ◽  
Theoretical Study ◽  
Static Stability ◽  
Governing Equations ◽  
Stability Threshold ◽  
Lennard Jones ◽  
The Stability ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Nonlocal Approach

Abstract On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.

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.

Effects of Initial Axial Stress on Nonlinear Vibration of Double-Walled Carbon Nanotubes Under Temperature Field

2011 ◽  
Vol 261-263 ◽  
pp. 842-847
Author(s):  
Yan Yan ◽  
Wen Quan Wang ◽  
Jian Rong Yang ◽  
Li Xiang Zhang
Keyword(s):  
Carbon Nanotubes ◽  
Temperature Field ◽  
Nonlinear Vibration ◽  
Axial Stress ◽  
Mechanical Behaviors ◽  
Amplitude Ratios ◽  
Frequency Curve ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Vdw Interaction

The paper studies the nonlinear vibrating mechanical behaviors of double-walled carbon nanotubes (DWCNTs) with the initial axial stress under the temperature field. The DWCNTs are modeled as double elastic shells coupled together through vdW interaction between inner and outer nanotubes. Based on the model, the relation between the amplitudes and the frequencies of the tubes is achieved. The results show that the initial axial stress could crucially affect the topological forms of the amplitude-frequency curve, whereas it is insensitive to the amplitude ratios in DWCNTs. Meanwhile, it is also concluded that the temperature change is significant for natural frequency, but weakly affects intertube frequency and amplitude ratios as well as amplitude-frequency curve.

Nonlinear Vibration of Single-Walled Carbon Nanotubes Under Magnetic Field by Stochastic Finite Element Method

2016 ◽  
Vol 16 (08) ◽  
pp. 1550046 ◽  
Author(s):  
T.-P. Chang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Longitudinal Magnetic Field ◽  
Small Scale ◽  
Stochastic Finite Element Method ◽  
Single Walled Carbon ◽  
Statistical Dynamic

In the present study, we investigate the statistical nonlinear dynamic behaviors of a single-walled carbon nanotube (SWCNT) subjected to a longitudinal magnetic field by considering the effect of geometric nonlinearity. We consider both the Young’s modulus of elasticity and mass density of the SWCNT as stochastic with respect to the position to actually characterize the random material properties of the SWCNT. In addition, we use the theory of nonlocal elasticity to investigate the small scale effect on the nonlinear vibration of the SWCNT. By using the Hamilton’s principle, the nonlinear governing equations of the SWCNT subjected to a longitudinal magnetic field are derived. We utilize the stochastic finite element method along with the perturbation technique to compute the statistical response of the SWCNT. Some statistical dynamic response of the SWCNT, such as the mean values and standard deviations of the midpoint deflections, are computed and checked by the Monte Carlo simulation, besides, the effects of the small scale coefficients, magnetic field and the elastic stiffness of matrix on the statistical dynamic response of the SWCNT are studied and discussed.

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