scholarly journals Study on the small-scale effect on wave propagation characteristics of fluid-filled carbon nanotubes based on nonlocal fluid theory

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401882332
Author(s):  
Yang Yang ◽  
Wuhuai Yan ◽  
Jinrui Wang
Keyword(s):  
Wave Propagation ◽  
Fluid Flow ◽  
Carbon Nanotube ◽  
Scale Effect ◽  
Strain Gradient ◽  
Small Scale ◽  
Beam Model ◽  
Governing Equations ◽  
Mode Wave ◽  
Fluid Theory

In this article, Timoshenko’s beam model is established to investigate the wave propagation behaviors for a fluid-conveying carbon nanotube when employing the nonlocal stress–strain gradient coupled theory and nonlocal fluid theory. The governing equations of motion for the carbon nanotube are derived. The small-scale influences induced by the nanotube are simulated by nonlocal and strain gradient effects, and the scale effect induced by fluid flow is first investigated applying nonlocal fluid theory. Numerical results obtained by solving the governing equations indicate that the nonlocal effect induced by the nanotube leads to wave damping and a decrease in stiffness, while the strain gradient effect contributes to wave promotion and an enhancement in stiffness. The scale effect caused by the inner fluid only leads to a decay for a high-mode wave since there is no influence from fluid flow on the low-mode wave. The numerical solution is validated by comparing with Monte Carlo simulation and interval analysis method.

Nonlinear Vibration Analysis of Microscale Functionally Graded Timoshenko Beams using the Most General form of Strain Gradient Elasticity

2013 ◽  
Vol 30 (2) ◽  
pp. 161-172 ◽  
Author(s):  
R. Ansari ◽  
M. Faghih Shojaei ◽  
V. Mohammadi ◽  
R. Gholami ◽  
H. Rouhi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Functionally Graded ◽  
Small Scale ◽  
Length Scale ◽  
Beam Model ◽  
Strain Gradient Elasticity ◽  
Governing Equations

ABSTRACTBased on the Timoshenko beam model, the nonlinear vibration of microbeams made of functionally graded (FG) materials is investigated under different boundary conditions. To consider small scale effects, the model is developed based on the most general form of strain gradient elasticity. The nonlinear governing equations and boundary conditions are derived via Hamilton's principle and then discretized using the generalized differential quadrature technique. A pseudo-Galerkin approach is used to reduce the set of discretized governing equations into a time-varying set of ordinary differential equations of Duffing-type. The harmonic balance method in conjunction with the Newton-Raphson method is also applied so as to solve the problem in time domain. The effects of boundary conditions, length scale parameters, material gradient index and geometrical parameters are studied. It is found that the importance of the small length scale is affected by the type of boundary conditions and vibration mode. Also, it is revealed that the classical theory tends to underestimate the vibration amplitude and linear frequency of FG microbeams.

scholarly journals Axisymmetric Wave Propagation Behavior in Fluid-Conveying Carbon Nanotubes Based on Nonlocal Fluid Dynamics and Nonlocal Strain Gradient Theory

2020 ◽  
Vol 8 (5) ◽  
pp. 773-780
Author(s):  
Yang Yang ◽  
Qihui Lin ◽  
Rongxin Guo
Keyword(s):  
Fluid Dynamics ◽  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Fluid Flow ◽  
Strain Gradient ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Nonlocal Stress ◽  
Axisymmetric Wave ◽  
Second Mode

Abstract Purpose Goal for the present research is investigating the axisymmetric wave propagation behaviors of fluid-filled carbon nanotubes (CNTs) with low slenderness ratios when the nanoscale effects contributed by CNT and fluid flow are considered together. Method An elastic shell model for fluid-conveying CNTs is established based on theory of nonlocal elasticity and nonlocal fluid dynamics. The effects of stress non-locality and strain gradient at nanoscale are simulated by applying nonlocal stress and strain gradient theories to CNTs and nonlocal fluid dynamics to fluid flow inside the CNTs, respectively. The equilibrium equations of axisymmetric wave motion in fluid-conveying CNTs are derived. By solving the governing equations, the relationships between wave frequency and all small-scale parameters, as well as the effects caused by fluid flow on different wave modes, are analyzed. Results The numerical simulation indicates that nonlocal stress effects damp first-mode waves but promote propagation of second-mode waves. The strain gradient effect promotes propagation of first-mode waves but has no influence on second-mode waves. The nonlocal fluid effect only causes damping of second-mode waves and has no influence on first-mode waves. Damping caused by nonlocal effects are most affect on waves with short wavelength, and the effect induced by strain gradient almost promotes the propagation of wave with all wavelengths.

Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory

2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Axial Compression ◽  
Buckling Load ◽  
Small Scale ◽  
Beam Model ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Nonlocal Continuum Theory ◽  
Walled Carbon Nanotubes

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

On the size-dependent nonlinear dynamics of viscoelastic/flexoelectric nanobeams

2020 ◽  
pp. 107754632095222
Author(s):  
Rasoul Bagheri ◽  
Yaghoub Tadi Beni
Keyword(s):  
Boundary Conditions ◽  
Viscoelastic Medium ◽  
Medium Effect ◽  
Small Scale ◽  
Beam Model ◽  
Governing Equations ◽  
Size Dependent ◽  
Flexoelectric Effect ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

In this study, size-dependent nonlinear forced vibration of viscoelastic/flexoelectric nanobeams has been investigated. By calculating enthalpy and kinetic energy and using Hamilton’s principle, the coupled governing equations of viscoelastic/flexoelectric nanobeams are derived along with dependent electrical and mechanical boundary conditions. Furthermore, to take the effects of the small scale into account, the nonclassical theory of continuous medium has been used and the Euler–Bernoulli beam model has been adopted to model the nanobeams. Finally, the governing equations are solved using numerical methods for distributed loaded and clamped–clamped boundary conditions. By comparing the results, it is determined that the parameters of the size effect and the viscoelastic medium effect can increase the vibrational frequency of the nanobeams. Also, the results show that the frequency of nanobeams outside of the viscoelastic medium strongly depends on the size-dependent parameters, and the increase in the length and thickness of the nanobeam decreases the frequency. The results also show that with the increasing flexoelectric effect, the amplitude of the nonlinear oscillation increases.

Investigation on Size Effect of Cantilever Carbon Nanotube

2012 ◽  
Vol 586 ◽  
pp. 3-9
Author(s):  
Ying Jing Liang ◽  
Qiang Han
Keyword(s):  
Carbon Nanotube ◽  
Scale Effect ◽  
Scale Effects ◽  
Elastic Shell ◽  
Small Radius ◽  
Small Scale ◽  
Moment Theory ◽  
Concentrated Load ◽  
Small Scale Effect ◽  
Analytical Expressions

Nonlocal elastic shell model based on the semi-moment theory is developed and applied to investigate the small scale effect on the bending problem of the cantilever carbon nanotube (CNT) with a vertical concentrated load applied at its tip. The small-scale effect is taken into account and is incorporated in the formulation. Analytical expressions of the stress are derived for the nonlocal elastic bending problem. It is obvious to observe significant small-scale effects on the stress resultants. The smaller the radius is, the more obvious the scale effect appears. The numerical results show that the scale effect cannot be ignored for CNTs of small radius.

Strain Gradient Finite Element Analysis on the Vibration of Double-Layered Graphene Sheets

2016 ◽  
Vol 13 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Wei Xu ◽  
Lifeng Wang ◽  
Jingnong Jiang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Strain Gradient ◽  
Virtual Work ◽  
Gradient Elasticity ◽  
Kirchhoff Plate ◽  
Small Scale ◽  
Graphene Sheets ◽  
Simply Supported

A nonlocal Kirchhoff plate model with the van der Waals (vdW) interactions taken into consideration is developed to study the vibration of double-layered graphene sheets (DLGS). The dynamic equations of multi-layered Kirchhoff plate are derived based on strain gradient elasticity. An explicit formula is derived to predict the natural frequency of the DLGS with all edges simply supported. Then a 4-node 24-degree of freedom (DOF) Kirchhoff plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration by the theory of virtual work. It can be directly used to predict the scale effect on the vibrational DLGS with different boundary conditions. A good agreement between finite element method (FEM) results and theoretical natural frequencies of the vibration simply supported double-layered graphene sheet (DLGS) validates the reliability of the FEM. Finally, this new FEM is used to investigate the effect of vdW coefficients, sizes, nonlocal parameters, vibration mode and boundary conditions on the vibration behaviors of DLGS.

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