Straight Single-walled Carbon Nanotubes Research Articles

Frequency analysis of FG-CNT–reinforced composite doubly curved panels on visco-Pasternak medium

In this paper, the free damped vibration behavior of doubly curved panels is investigated, while reinforcements are aligned and straight single-walled carbon nanotubes with uniform and functionally graded distributions under four different patterns through thickness. The extended rule of mixtures is employed to achieve effective material properties. Hamilton principle and third-order shear deformation theory of Reddy are used for governing equations of motions of spherical, cylindrical, hyperboloid and paraboloid panels resting on visco-Pasternak medium. A semi-analytical approach with an iterative numerical algorithm is implemented to figure out frequencies and modal loss factors of eigenvalue problem. To verify, the present results are compared with those that are obtained via first-order shear deformation theory for flat, cylindrical, and spherical panels. Also, the influence of shallowness, thickness, curvature, aspect ratios, distribution and content of carbon nanotubes, and viscoelastic medium on natural frequency and damping capability of panels are examined via numerical examples. For the first time, the crossing phenomena of natural frequencies and modal loss factors of FG-CNT–reinforced composite panels with external damping under higher-order theory assumptions are presented. Results show that hyperboloid panels with high aspect, shallowness, and low thickness ratios are susceptible to follow inharmonic motion rather than a harmonic one.

Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

The effect of multi-directional nanocomposite materials on the vibrational response of thick shell panels with finite length and rested on two-parameter elastic foundations

The main purpose of this paper is to investigate the effect of bidirectional continuously graded nanocomposite materials on free vibration of thick shell panels rested on elastic foundations. The elastic foundation is considered as a Pasternak model after adding a shear layer to the Winkler model. The panels reinforced by randomly oriented straight single-walled carbon nanotubes are considered. The volume fractions of SWCNTs are assumed to be graded not only in the radial direction, but also in axial direction of the curved panel. This study presents a 2-D six-parameter power-law distribution for CNTs volume fraction of 2-D continuously graded nanocomposite that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. The material properties are determined in terms of local volume fractions and material properties by Mori–Tanaka scheme. The 2-D differential quadrature method as an efficient numerical tool is used to discretize governing equations and to implement boundary conditions. The fast rate of convergence of the method is shown and results are compared against existing results in literature. Some new results for natural frequencies of the shell are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded nanocomposite volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded nanocomposite materials.

Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube

This work reports wave propagation in the nanocomposite cylinders that reinforced by straight single-walled carbon nanotubes based on a mesh-free method. Moving least square shape functions have been used for approximation of displacement field in weak form of motion equation. The straight carbon nanotubes (CNTs) are assumed to be oriented in specific or random directions or locally aggregated into some clusters. In this simulation, an axisymmetric model is used and also the volume fractions of the CNTs and clusters are assumed to be functionally graded along the thickness. So, material properties of the carbon nanotube reinforced composite cylinders are variable and estimated based on the Eshelby-Mori-Tanaka approach. The effects of orientation, aggregation and volume fractions of the functionally graded clusters and CNTs on dynamic behavior of nanocomposite cylinders are studied. This study results show that orientation and aggregation of CNTs have significant effects on the effective stiffness and dynamic behaviors.

Elasticity solution of functionally graded carbon nanotube-reinforced composite cylindrical panel subjected to thermo mechanical load

Thermoelastic analysis of composite cylindrical panel reinforced by single walled carbon nanotube (SWCNT) with simply supported edges by using three-dimensional theory of elasticity. Thermoelastic constant of carbon nanotube (CNT) as well as polymer matrix are assumed to be temperature independent. The volume fractions of oriented, straight SWCNTs are assumed to be uniformly distributed (UD) and or graded in the thickness direction according to four kinds of CNT distributions. The effective material properties of the nanocomposite cylindrical panel are based on rule of mixture. At first temperature distribution in three dimensions is obtained by solving heat conduction differential equation with variable coefficient. By applying Fourier series expansion to the stress and displacement fields along the axial and circumferential direction and state space technique along the radial direction thermoelastic analysis is carried out. Moreover, effects of volume fraction of carbon nanotube, uniform distribution and functionally graded distribution of CNT, mid radius to thickness ratio, length to mid radius ratio, thermal and mechanical surface boundary conditions on bending behavior of FG-CNTRC cylindrical panel are also examined.

Nonstraight nanochannels transfer water faster than straight nanochannels.

Understanding the flow of liquids and particularly water in nanochannels is important for scientific and technological applications, such as for filtration and drug delivery. Here we perform molecular dynamics simulations to investigate the transfer of single-file water molecules across straight or nonstraight single-walled carbon nanotubes (SWCNTs). In contrast with the macroscopic scenario, the nonstraight nanostructure can increase the water permeation. Remarkably, compared with the straight SWCNT, the nonstraight SWCNT with the minimal bending angle of 35° in the simulations can enhance the water transport up to 3.5 times. This enhancement mainly originates from the Lennard-Jones interaction between water molecules and nonstraight nanostructures. Our work offers an additional freedom to design high-flux nanochannels by choosing nonstraight nanostructures and provides an insight into water flow across biological water nanochannels, which are often nonstraight since they are composed of integral membrane proteins.

In search of molecular scale devices: Theoretical study of linearly fused straight single-walled carbon nanotube junctions based on the pentagon/heptagon pair defects

The structural and electronic properties of topological defect of straight intramolecular junctions between two zigzag single-walled carbon nanotubes (SWCNT-IMJ) were studied theoretically. The interfacial junctions can be constructed by fusing two zigzag tubes that differ in helicities and diameters. In the present study, one segment is kept constant by using the (5,0) nanotube, while varying another segment from (6,0) to (10,0). Practically, these (5,0)//(m,0) structures are composed of one or more pentagon/heptagon pairs as “defect” functioning to fuse other perfect hexagonal lattices. It was found that, at the interfacial junctions the 5/7 pair defects induce modified rehybridization of the carbon–carbon networks, which directly affect the geometric and electronic properties. Consequently, the electronic structures are dependent on the variation of diameter and length of carbon nanotubes. Analyses of the electronic structures reveal that the HOMO and LUMO levels exhibit the even–odd “quantum size” oscillation versus varying nanotube chiralities, even with increasing length of nanotubes. The energy gap that indicates metallic or semi-conducting behavior depends on correlation between the tubes indices and tubule length. The NBO analysis has revealed that topological pair defects variation could be an important role for altering the electronic characteristics on these intramolecular junctions. By screening all structures based on their electronic structure diagrams and orbital visualization, we have found that the straight (5,0)//(7,0) junction should be suitable as a molecular rectifying diode. However, other junction structures can also be useful with appropriate tuning of the bias voltage. The outcome of this study would be of help as a knowledge base in the field of carbon nanomaterials molecular electronics.

Vibration Analysis of Randomly Oriented Carbon Nanotube Based on FGM Beam Using Timoshenko Theory

The carbon nanotube (CNT) reinforced functionally graded materials (FGM) are expected to be the new generation materials having wide range of unexplored potential applications in various technological areas such as aerospace and structural and chemical industry. The present work deals with the finite element modeling and free vibration analysis of CNT based functionally graded beam using three-dimensional Timoshenko beam theory. It has been assumed that the material properties of CNT based FG beam vary only along the thickness and these properties are evaluated by rule of mixture. The extended Hamilton principle has been applied to find out the governing equations of CNT based FG beam. Finite element method is used to solve governing equation with the exact shape functions. Initial analysis deals with CNTs assumed to be oriented along the length direction only. But practically it is not possible. So, further work deals with the free vibration analysis of functionally graded nanocomposite beams reinforced by randomly oriented straight single walled carbon nanotubes (SWCNTs). The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. Results are presented in tabular and graphical forms to show the effects of carbon nanotube orientations, slenderness ratios, and boundary conditions on the dynamic behavior of the beam.

Mixed Navier-layerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates

The three-dimensional free vibration and static analysis of the laminated plates with functionally graded (FG) carbon nanotube reinforced composite (CNTRC) layers is presented using a semi-analytical approach. The individual layers are assumed to be made from a mixture of aligned and straight single-walled carbon nanotubes (CNTs) with volume fractions graded in the thickness direction, and an isotropic matrix. The effective material properties of the resulting FG-CNTRC layers are estimated through a micromechanical model. The through-the-thickness variations of the displacement components are accurately modeled using a layerwise-differential quadrature method, and their in-plane variations are approximated using the trigonometric series. After demonstrating the convergence and accuracy of the method, the effects of geometrical parameters, type of CNTs distribution and volume fractions, and also lamination scheme on the natural frequencies, displacement and stress components of the FG-CNTRC layered plates are investigated.

Influence of equivalent continuum model based on the Eshelby-Mori-Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates

Most of the early studies on plates vibration were focused on two-dimensional (2D) theories; these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3D elasticity solution for free vibration analysis of 2D continuously graded carbon nanotube-reinforced (CGCNTR) annular plates resting on a two-parameter elastic foundation. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness and radial directions. Various material profiles along the thickness and radial directions are illustrated using the 2D power-law distribution. An equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). A semi-analytical approach composed of 2D differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The convergence of the method is demonstrated and comparisons are made between the present results and results reported by well-known references and have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach to reveal the impacts of the volume fractions of oriented CNTs and different CNTs distributions on the vibrational characteristics of annular plates which are assumed to be graded in one (or more) direction(s). POLYM. COMPOS., 35:1644–1661, 2014. © 2013 Society of Plastics Engineers

Thermal conductivity of carbon nanocoils

The extreme reduction of the thermal conductivity by defects and folds in carbon nanocoils (CNCs) are first demonstrated using nonequilibrium molecular dynamics simulations. The thermal conductivity for two different defect types with five different folds in the CNCs is extensively studied and the maximum reduction can be up to 70% at both room temperature and 600 K by comparison of the corresponding straight single-walled carbon nanotubes. We reveal that the phonon scattering by coupled defects and folds can govern the reduction of the thermal conductivity by calculating phonon polarization vectors.

Structural model of semi-metallic carbon nanotubes

Electronic band structure and electronic density of states (DOS) of single-walled helically coiled carbon nanotubes (HCCNTs) are numerically calculated by symmetry implemented density functional tight binding method. It is found that unlike straight single-walled carbon nanotubes, single-walled HCCNTs can be semi-metallic, having high DOS at Fermi level. We show that this is a consequence of the local structure of HCCNTs, i.e., that by changing positions of pentagons and heptagons within a monomer, transitions between metallic, semi-metallic, quasi-metallic, and semiconducting structures can be made.

Eshelby-Mori-Tanaka approach for vibrational behavior of functionally graded carbon nanotube-reinforced plate resting on elastic foundation

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of functionally graded (FG) nanocomposite plates reinforced by randomly-oriented straight single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation are considered. Material properties are graded in the thickness direction of the plate according to the volume fraction power law distribution. An embedded carbon nanotube (CNT) in a polymer matrix and its surrounding inter-phase which is perfectly bonded to surrounding resin is replaced with an equivalent fiber to predict the mechanical properties of the carbon nanotube/polymer composite. The Mori-Tanaka approach is employed to calculate the effective elastic moduli of the plate. The natural frequencies of the plate are obtained by means of the generalized differential quadrature (GDQ) method. Detailed parametric studies have been carried out to investigate the influences of the CNT volume fraction, Winkler foundation modulus, shear elastic foundation modulus and various geometrical parameters on the vibration behavior of the functionally graded carbon nanotube-reinforced (FG-CNTR) plates.

The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method

In this paper, axisymmetric natural frequencies of nanocomposite cylinders reinforced by straight single-walled carbon nanotubes are presented based on a mesh-free method. The straight carbon nanotubes (CNTs) are oriented, aligned or randomly or locally aggregated into some clusters. Volume fractions of the CNTs and clusters are assumed to be functionally graded along the thickness, so material properties of the carbon nanotube reinforced composite cylinders are variable and are estimated based on the Eshelby–Mori–Tanaka approach. In the mesh-free analysis, moving least squares shape functions are used for an approximation of the displacement field in the weak form of motion equation, and the transformation method is used for the imposition of essential boundary conditions. The effects of orientation and aggregation of the functionally graded CNT are studied. It is observed that kind of distributions, aggregation or even randomly orientations of CNTs has significant effect on the effective stiffness and frequency parameter.

Mechanical Buckling of Thick Composite Plates Reinforced with Randomly Oriented, Straight, Single-Walled Carbon Nanotubes Resting on an Elastic Foundation using the Finite Strip Method

AbstractThis paper is devoted to the mechanical buckling analysis of thick composite plates under straight single-walled carbon nanotubes reinforcement with uniform distribution and random orientations resting on an elastic foundation. To develop the fundamental equations, the finite strip method, along with third-order shear deformation theory, is employed, and the total potential energy is minimized, which leads to an eigenvalue problem. The elastic foundation is modeled by classical and two-parameter simulations. For deriving the effective modulus of composite plates reinforced with carbon nanotubes, a method is used in which each straight carbon nanotube is modeled as a fiber with transversely isotropic elastic properties. The results of the numerical experiments, including the critical buckling loads for thick rectangular composite plates reinforced by carbon nanotubes with various boundary conditions and different volume fractions of nanotubes, are provided, and the positive effect of using carbon n...

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory

Based on the third-order shear deformation theory (TSDT), the investigation of the free vibration response of a continuously graded carbon nanotube-reinforced (CGCNTR) cylindrical shell is presented. The volume fractions of randomly oriented straight single-walled carbon nanotubes are assumed to be graded in the thickness direction. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The Mori–Tanaka scheme as an accurate micromechanics model is used for estimating the homogenized material properties of nanocomposites reinforced with equivalent fibers. The equations of motion and the associated boundary conditions are derived using the Hamilton’s principle based on TSDT. The discretization of the system by means of the Generalized Differential Quadrature Method leads to a standard linear eigenvalue problem. Detailed parametric studies have been carried out to study the impacts of the various types of equivalent fiber distribution, different boundary conditions and geometrical parameters on the vibration characteristics of CGCNTR cylindrical shells. The interesting finding of the present study is that the graded CNT volume fractions with symmetric distribution through the shell thickness have high capabilities to reduce or increase the natural frequency in comparison with uniformly and asymmetric CNT distribution.

Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes

In this paper, the mechanical buckling of a functionally graded nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs) subjected to uniaxial and biaxial in-plane loadings is investigated. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction and vary continuously and smoothly according to two types of the symmetric carbon nanotubes volume fraction profiles. The material properties of SWCNT are determined according to molecular dynamics (MDs), and then the effective material properties at a point are estimated by either the Eshelby–Mori–Tanaka approach or the extended rule of mixture. The equilibrium and stability equations are derived using the Mindlin plate theory considering the first-order shear deformation (FSDT) effect and variational approach. The results for nanocomposite plate with uniformly distributed CNTs, which is a special case in the present study, are compared with those of the symmetric profiles of the CNTs volume fraction. A numerical study is performed to investigate the influences of the different types of compressive in-plane loadings, CNTs volume fractions, various types of CNTs volume fraction profiles, geometrical parameters and different types of estimation of effective material properties on the critical mechanical buckling load of functionally graded nanocomposite plates.

Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels

In this paper, natural frequencies characteristics of a continuously graded carbon nanotube-reinforced (CGCNTR) cylindrical panels based on the Eshelby–Mori–Tanaka approach is considered. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this research work, an equivalent continuum model based on the Eshelby–Mori–Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The CGCNTR shell is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The novelty of the present work is to exploit Eshelby–Mori–Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various mid radius-to-thickness ratio, shell angle, length-to-mean radius ratio and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR cylindrical panels. The interesting and new results show that continuously graded oriented CNTs volume fractions can be utilized for the management of vibrational behavior of structures so that the frequency parameters of structures made of such material can be considerably improved than that of the nanocomposites reinforced with uniformly distributed CNTs.

Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models

The transverse vibration of a single-walled carbon nanotube (SWCNT) with light waviness along its axis is modeled by the nonlocal Euler-Bernoulli and Timoshenko beam theory. Unlike the Euler-Bernoulli beam model (EBM), the effects of transverse shear deformation and rotary inertia are considered within the framework of the Timoshenko beam model (TBM). The surrounding elastic medium is described as both Winkler-type and Pasternak-type foundation models. The governing equations are derived using Hamilton’s principle, and the Galerkin method is applied to solve these equations. According to this study, the results indicate that the frequency calculated by TBM is lower than that obtained by EBM. Detailed results show that the importance of transverse shear deformation and rotary inertia become more significant for stocky SWCNTs with clamped-clamped boundary conditions. Moreover, the influences of the amplitude of waviness, nonlocal parameter, medium constants, boundary conditions and aspect ratio are analyzed and discussed. It is shown that waviness in the curved SWCNT causes an obvious increase in the natural frequency in comparison with the straight SWCNT, especially for a compliant medium, pinned-pinned boundary condition, short SWCNT and large nonlocal coefficient.