Nanotube Volume Fraction Research Articles

Dynamic Response of Functionally Graded Carbon Nanotube-Reinforced Hybrid Composite Plates

Dynamic instability behavior of functionally graded carbon nanotube reinforced hybrid composite plates subjected to periodic loadings is studied. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunctions transforms. With the Mathieu equations, the dynamic instability regions of hybrid nanocomposite plates are determined by using the Bolotin’s method. Results reveal that the dynamic instability is significantly affected by the carbon nanotube volume fraction, layer thickness ratio, bending stress, static and dynamic load parameters. The effects of important parameters on the instability region and dynamic instability index of hybrid nanocomposite plates are discussed.

Free vibration analysis of rotating FG-CNT reinforced composite beams in thermal environments with general boundary conditions

The linear free vibration of rotating FG-CNTRC Timoshenko beams in the thermal environments with general boundary conditions is investigated. The classical and non-classical boundary conditions of the rotating beams are simulated by the artificial spring technique. The first order shear deformation theory is employed to establish the governing equations and the temperature depended material properties of the FG-CNTRC are considered. By adopting the Rayleigh-Ritz method together with the artificial technique, a unified solution for the free vibration of rotating beams is carried out. The allowance displacement functions of the rotating beams with different boundary conditions are unified expanded in the form of Jacobi polynomials. The results obtained by the present solution are compared with those in the existing literature to evaluate the accuracy of the proposed approach. The effects of volume fraction and distribution types of carbon nanotubes, rotating speed, temperature, slenderness ratio and hub ratio on the vibration behaviors of the beams are investigated. The stable regions of rotating FG-CNTRC beams in thermal environment are achieved. Furthermore, a general and effective solution for the vibration analysis of rotating FG-CNTRC beams with classic and non-classic boundary conditions is proposed. The main advantage of the proposed solution is that there is no need to change the displacement trial function and solution equations for the beams with different boundary conditions and it can be also applied to analyze the vibration behaviors of other structures.

Dynamics of water conveying single-wall carbon nanotubes and magnetite nanoparticles subject to induced magnetic field: A bioconvective model for theranostic applications

The current study presents a bioconvective model to investigate the dynamics of water conveying single-wall carbon nanotubes (SWCNTs) and magnetite nanoparticles on the stagnation point flow along a stretching sheet subject to chemical reaction, viscous dissipation, induced magnetic field, and stratification effects. With applications ranging from biomedical imaging, hyperthermia, targeted drug delivery, and cancer therapy, the present study provides a theoretical perspective that is beneficial in biomedical engineering. Relevant similarity formulas are effectuated in converting the governing equations into a system of ODEs and are further treated numerically using the Runge-Kutta-Fehlberg method with the shooting technique. Illustrations on the effect of temperature, microorganisms, concentration, and velocity profiles due to the varying parameter values are achieved with the aid of graphs. It is observed that augmenting volume fraction of single-wall carbon nanotube and magnetite nanoparticles exhibit a constructive effect on temperature profile, which helps in killing cancerous cells. Further, the simultaneous impact of effectual parameters on surface drag, heat transfer rate, mass transfer rate, and microorganism density number is studied using graphs. It is seen that augmenting chemical reaction parameter tends to elevate the mass transfer rate and the microorganism density number.

A Multi-Scale Method for Designing Hybrid Fiber-Reinforced Composite Drive Shafts with Carbon Nanotube Inclusions

In this paper, the modal and linear buckling analysis of a laminated composite drive shaft reinforced by 11 multi-walled carbon nanotubes (MWCNTs) was carried out using an analytical approach, as well as the finite element method (FEM). The theoretical model is based on classical laminated theory (CLT). The fundamental frequency and the critical buckling torque were determined for different fiber orientation angles. The Halpin–Tsai model was employed to calculate the elastic modulus of composites having randomly oriented nanotubes. The effect of various carbon nanotube (CNT) volume fractions in the epoxy resin matrix on the material properties of unidirectional composite laminas was also analyzed. The fundamental frequency and the critical buckling torque obtained by the finite element analysis and the analytical method for different fiber orientation angles were in good agreement with each other. The results were verified with data available in the open literature, where possible. For the first time in the literature, the influence of CNT fillers on various composite drive shaft design parameters such as the fundamental frequency, critical speed, and critical buckling torque of a hybrid fiber-reinforced composite drive shaft is finally predicted.

Rheological, Dynamic and Tensile Mechanical Properties of Recycled Styrofoam Loaded with Carbon Nanotubes

Styrofoam was recycled and then loaded with different volume fractions of multiwalled carbon nanotubes (MWC-NTs). The frequency dependence of complex viscosity η*, storage modulus E/ and loss modulus E// were studied. All of them were increased with increasing MWCNTs concentration. The dependence of the complex viscosity on CNTs concentration was found to obey the rheological percolation behavior with low percolation threshold and depends on frequency. The addition of MWCNTs to recycled Styrofoam did not change the glass transition temperature. The tensile properties of all composites were studied at different temperatures. Stress-strain curves at temperatures 30, 50, 70 and 90 °C showed brittle behavior. The elastic modulus, ultimate strength, strain at break, and energy density to break were increased with increasing both CNTs concentration and temperature up to 90 °C. The elastic modulus had a tensile percolation behavior with a threshold value close to that obtained for η*. Plastic deformation of all composites took place at 105 °C and sharp decrease in both E and σb was observed. Conversely, sharp increase in both strain at break and energy density to break was observed at temperature 105 °C. The material at this temperature was converted from polydomain to monodomain configuration.

Dynamic modelling and analysis of smart carbon nanotube-based hybrid composite beams: Analytical and finite element study

In this work, the carbon nanotube-based hybrid carbon fibre-reinforced composite smart beam constraining the layer of an active constrained layer damping treatment is investigated using an in-house finite element model based on first-order shear deformation theory. The effect of in-plane and transverse-plane actuation of the integrated active constrained layer damping treatment layer on the damping characteristics of the novel smart cantilever hybrid carbon fibre-reinforced composite beam is considered. The parameters affecting the damping characteristics of the hybrid carbon fibre-reinforced composite substrate beam such as the volume fraction of both carbon nanotubes and carbon fibre, and the aspect ratio are also studied. Besides, the micromechanical model based on the mechanics of materials approach is developed to estimate the effective elastic coefficient of novel hybrid carbon fibre-reinforced composite lamina. The effective properties of hybrid carbon fibre-reinforced composite are predicted quantitatively by considering non-bonded interaction formed between carbon nanotubes and the polymer matrix. It is revealed that due to the incorporation of carbon nanotubes into the epoxy matrix, the effective longitudinal, transverse and shear properties of the hybrid carbon fibre-reinforced composite lamina are significantly enhanced. Our outcomes explore that the damping performance of the laminated hybrid carbon fibre-reinforced composite smart beam considering the incorporation of carbon nanotubes shows substantial improvement as compared to the base composite. To bring more clarity, the quantitative relative performance of hybrid carbon fibre-reinforced composite and base composite is presented. Our fundamental analysis sheds the light on the opportunities of developing efficient, high-performance and lightweight carbon nanotubes-based micro-electro-mechanical systems smart structures such as sensors, actuators and distributors.

Convective heat transfer for Peristaltic flow of SWCNT inside a sinusoidal elliptic duct.

A mathematical model is presented to analyse the flow characteristics and heat transfer aspects of a heated Newtonian viscous fluid with single wall carbon nanotubes inside a vertical duct having elliptic cross section and sinusoidally fluctuating walls. Exact mathematical computations are performed to get temperature, velocity and pressure gradient expressions. A polynomial solution technique is utilized to obtain these mathematical solutions. Finally, these computational results are presented graphically and different characteristics of peristaltic flow phenomenon are examined in detail through these graphs. The velocity declines as the volume fraction of carbon nanotubes increases in the base fluid. Since the velocity of fluid is dependent on its temperature in this study case and temperature decreases with increasing volumetric fraction of carbon nanotubes. Thus velocity also declines for increasing volumetric fraction of nanoparticles.

A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates

The paper presents a novel nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates. To observe the length scale and size-dependency effects of nanostructures, the nonlocal strain gradient theory (NSGT) is considered. The present model is efficient to capture both nonlocal effects and strain gradient effects in nanoplate structures. In addition, the material properties of the FG-CNTRC are assumed to be graded in the plate thickness direction. Based on the higher order shear deformation theory (HSDT), the weak form of the governing equations of motion of the nanoplates is presented using the principle of virtual work. Afterward, the natural frequency and deflection of the nanoplates are made out of isogeometric analysis (IGA). Thanks to higher order derivatives and continuity of NURBS basic function, IGA is suitable for the weak form of NSGT which requires at least the third-order derivatives in approximate formulations. Effects of nonlocal parameter, strain gradient parameter, carbon nanotube (CNT) volume fraction, distributions of CNTs and length-to-thickness ratios on deflection and natural frequency of the nanoplates are examined and discussed in detail. Numerical results are developed to show the phenomenon of stiffness-softening and stiffness-hardening mechanisms of the present model.

Dynamic Analysis of Carbon Nanotube-Reinforced Multilayer Composite Plates

The paper studied the analysis of vibrations of rectangular carbon nanotube-reinforced composite plates. To this end, a three-layer nanocomposite plate - two layers with the targeted distribution of carbon nanotubes as FG-X at the top and bottom and a layer without an amplifier in the middle of the plate - were analyzed. The governing equations for this problem are based on First-order Shear Deformation Theory (FSDT). The distribution of nanotubes on these plates is as targeted FG-X. The effect of various types of SWCNTs distributions in the direction of thickness on the vibrational behavior of nanocomposite plates was examined. The effective properties of nanocomposite materials Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) were estimated using the rule of mixtures. Detailed parametric studies were performed to determine the effects of the volume fraction of carbon nanotubes and the thickness-to-length ratio of the plate on the natural frequency responses and the shape of the plate mode. The equations obtained in this problem were coded in MATLAB software, the nanocomposite plate was modelled in ABAQUS software, and the comparison of the results obtained from the numerical solution with ABAQUS software showed relatively right consistency with the results obtained from the analytical solution.

Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes.

This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nanotubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations.

Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson’s ratio auxetic honeycombs core and CNTRC face sheets

Recently, auxetic cellular solids in the forms of honeycombs and carbon nanotube reinforced composite (CNTRC) have great potential in a diverse range of applications. This paper studies the nonlinear free and forced vibration of sandwich cylindrical panel on visco-Pasternak foundations in thermal environment subjected to blast load The sandwich cylindrical panel consists of auxetic honeycombs core layer and two CNTRC face sheets. The Poisson’ ratio of the auxetic core is negative and the material properties of CNTRC face sheets are assumed to continuously vary in the thickness direction according to four different types of linear functions. The blast load is determined from the distance of the center of blast to center of the structure and the mass of explosive materials. The fundamental equations are established based on Reddy’s higher order shear deformation shell theory taking into account the effect of initial imperfection and visco-Pasternak foundations. The Galerkin and Runge–Kutta methods are used to obtain the nonlinear dynamic response and the natural frequency of the sandwich cylindrical panel. The numerical results show the effect of geometrical parameters, visco foundations, initial imperfection, temperature increment, nanotube volume fraction and blast load on the nonlinear vibration characteristics of the sandwich cylindrical panel. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

Natural convection nanofluid flow with heat transfer analysis of carbon nanotubes–water nanofluid inside a vertical truncated wavy cone

The flow of heat transfer study of carbon nanotubes (CNTs)–water nanofluid over vertical truncated wavy cone is considered. The present boundary layer power law fluid is analyzed near the truncated wavy cone. The considered cone is wavy in physical configuration and placed in a vertical direction. Moreover, nanosized particles of CNTs suspended into water (base fluid) are transporting in two directions, which are modeled by using Boussinesq's approximation. Coordinate transformation is applied in order to shift the wavy surface to a flat surface. Then governing equation dealing with the momentum of nanofluid along with thermal stratification are reduced in dimensionless form by using appropriate transformation. Results point out that the thickness of thermal boundary layer decreases by increasing the value of volume fraction of carbon nanotubes. Finally, the obtained solution is related through a graphical survey, and it is inferred that the investigation is in good accordance with the current literature.

Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the two-parameter elastic foundation (T-P-EF). It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs, based on a generalized first-order shear deformation shell theory (FSDST) which includes shell-foundation interaction. By adopting the extended mixing rule, the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters. Three carbon nanotube distribution in the matrix, i.e. uniform distribution (U) and V and X-types linear distribution are taken into account. The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads (CBLs) of the structure selected here. The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF. Finally, a parametric study is carried out to study the influences of the foundation parameters, the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

Dynamic simulation of a viscoelastic multi-phase nanocomposite reinforced cantilever spinning disk

This research's objective is a theoretical investigation into the frequency characteristics of the rotary multi-hybrid nanocomposite reinforced (MHCR) cantilever disk (MHCRCD). According to the Kelvin-Voight model, the presented structure is modeled as a disk covered by the viscoelastic foundation. Also, due to rotation, the centrifugal and Coriolis influences are investigated. For obtaining the effective Poisson ratio, and mass density, the role of mixture is employed. As well as this, the Halpin-Tsai micromechanics model is presented for modeling the effective Young module of the MHCRCD. Hamilton’s principle is established for obtaining the governing equations, and various boundary conditions of the rotary MHCRCD. Finally, the generalized differential quadrature method (GDQM) is employed to obtain eigenvalue and eigenvectors of the rotary viscoelastic MHCRCD. In the current research, simply-simply, and clamped-free (cantilever) boundary conditions are applied to edges and R = Ri , R = R0 , respectively. The results demonstrate that fibers’ angle of carbon, carbon nanotubes’ volume fraction, angular velocity, and patterns of carbon nanotubes (CNTs) have a marvelous impact on the frequency and amplitude behavior of the rotary MHCRCD. As an applicable result in related industries, the influence of the angular velocity of the rotary MHCRCD is more impressive in the higher values of the radius ratio.

Влияние углеродных нанотрубок на микроструктуру и трещиностойкость наноструктурной оксидной керамики

The structure and properties of ceramics based on zirconium dioxide stabilized yttrium oxide with the addition of high-modulus inclusions of carbon nanotubes were investigated. The composite materials were obtained by spark plasma sintering. The introduction of carbon nanotubes provides a slight decrease in the density and grain size of ceramics. Growth of volume fraction of carbon nanotubes leads to increase of mechanical properties of ceramic composites. The highest values of mechanical properties were obtained by the introduction of 5 vol.% of carbon nanotubes and were E = (246±8) GPa, H = (12.7±0.21) GPa, K 1 CI = (12.1±0.35) MPa∙m1/2, K 1 CN = (7.8±0.29) MPa∙m1/2. The increase of fracture toughness when carbon nanotubes are introduced into the ceramic matrix is caused by two dissipative mechanisms - phase transformation from tetragonal to monoclinic modification of ZrO2 and crack bridging. As the amount of introduced additive increases, the contribution of martensitic transformation in fracture resistance decreases, which is associated with a decrease in the grain size of the tetragonal zirconium dioxide phase and, accordingly, its transition to a stable state.

Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam

This work focused on the novel numerical tool for the bending responses of carbon nanotube reinforced composites (CNTRC) beams. The higher order shear deformation beam theory (HSDT) is used to determine strain-displacement relationships. A new exponential function was introduced into the carbon nanotube (CNT) volume fraction equation to show the effect of the CNT distribution on the CNTRC beams through displacements and stresses. To determine the mechanical properties of CNTRCs, the rule of the mixture was employed by assuming that the single-walled carbon nanotubes (SWCNTs)are aligned and distributed in the matrix. The governing equations were derived by Hamilton's principle, and the mathematical models presented in this work are numerically provided to verify the accuracy of the present theory. The effects of aspect ratio (l/d), CNT volume fraction (Vcnt), and the order of exponent (n) on the displacement and stresses are presented and discussed in detail. Based on the analytical results. It turns out that the increase of the exponent degree (n) makes the X-beam stiffer and the exponential CNTs distribution plays an indispensable role to improve the mechanical properties of the CNTRC beams.

Vibration analysis and control of micro porous beam integrated with FG-CNT distributed piezoelectric sensor and actuator

In this study, the active control and vibration analysis of a micro sandwich beam based on modified couple stress theory (MCST) are investigated. The core of sandwich structure is porous and the face sheets are made from piezoelectric material and reinforced by carbon nanotubes. The generalized rule of mixture is employed to predict the mechanical and electrical properties of a micro sandwich composite beam. Based on Hamilton's principle, the governing equations of motion for a micro Reddy beam are derived and active control is considered by the state space representation of the system. The results of this research show that the porosity coefficient, porosity distributions, carbon nanotubes (CNTs) volume fraction, CNTs distributions, the material length scale parameter and different face sheet and core thicknesses effect on the natural frequencies, the resonance phenomenon, settling time and deflection response of system. This research can provide a valuable background for further experimental studies as a basic investigation for applications of a micro sandwich beams in the field of micro robots. Also the results are potentially useful for active control, preventing the resonance phenomenon, design and optimization of micro sandwich beams.

Optimal Design of CNT-Nanocomposite Nonlinear Shells.

Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to accurately describe the point-wise material distribution. The sensitivity to geometrical imperfections is also investigated. The optimization is carried out making use of the Global Convergent Method of Moving Asymptotes. The extensive numerical analyses show that varying the volume fraction distribution as well as the CNTs orientation can lead to significantly enhanced performances towards the loss of elastic stability making these lightweight structures more stable. The most striking result is that for curved shells, the unstable postbuckling response of the baseline material can be turned into a globally stable response maintaining the same amount of nanostructural reinforcement but simply tailoring strategically its distribution.

Optical Response of Ultrathin Periodically Aligned Single-Wall Carbon Nanotube Films

AbstractWe present a semi-analytical expression for the dielectric response function of quasi-2D ultrathin films of periodically aligned single-walled carbon nanotubes. We derive the response function in terms of the individual nanotube conductivity, plasma frequency, and the volume fraction of carbon nanotubes in the film. The real part of the dielectric response function is negative for a sufficiently wide range of the incident photon energy, indicating that the film behaves as a hyperbolic metamaterial. Inhomogeneous broadening increases the effect.

Simultaneous Influence of Hall and Wall Characteristics in Peristaltic Convective Carbon–Water Flow Subject to Soret and Dufour Effects

Peristalsis of carbon nanotubes (SWCNTs, MWCNTs) submerged in water through an inclined asymmetric channel is addressed in the current work. Such mechanism is disclosed in the presence of Hall effect, viscous dissipation, and Soret and Dufour effects. Convective heat transfer at the boundaries is incorporated by utilizing efficient thermal conductivity of nanoliquid. Low Reynolds number and long wavelength approximation are used for mathematical modeling. Resulting nonlinear set of equations is solved for pressure gradient, velocity, temperature and concentration. Impact of various variables on the axial velocity, pressure rise, pressure gradient, temperature, concentration, heat transport at boundaries and streamlines are discussed via their respective curves. Comparison between SWCNTs (single-wall carbon nanotubes) and MWCNTs (multiwall carbon nanotubes) is documented. Furthermore, submerging carbon nanotubes in water declines the velocity and temperature. In addition, heat transfer at the boundaries enhances by increasing volume fraction of carbon nanotubes. SWCNTs nanofluid shows higher velocity and concentration when compared with MWCNTs nanofluid. MWCNTs nanoliquid displays higher temperature than SWCNTs nanoliquid.