Volume Fraction Of Carbon Nanotubes Research Articles

The effect of negative Poisson’s ratio on the low-velocity impact response of an auxetic nanocomposite laminate beam

In this paper, an investigation on the low-velocity impact (LVI) response of a shear deformable beam laminated by carbon nanotube reinforced composite (CNTRC) layers is performed. The composite beam is “auxetic” due to the negative out-of-plane Poisson’s ratio (NPR) through special symmetric stacking sequences of layers that are designed based on the Classical Laminate Theory. To study the effect of the out-of-plane NPR on the LVI response of the composite beam, a newly defined Hertz model is developed. The motion equations of Karman type for the CNTRC laminate beam are derived in the framework of the Reddy beam theory and solved by means of a two-step perturbation approach while the dynamic equation of the impactor is built on Newton’s Law. Since temperature-dependent material properties of both carbon nanotube (CNT) and matrix are employed, the thermal influence on the LVI behavior is also investigated. Moreover, a piece-wise method is employed herein to investigate the effect of functionally graded (FG) patterns of the CNT reinforcements on the impact response. Numerical results elucidating the effects of temperature, FG distribution, and CNT volume fraction on the out-of-plane Poisson’s ratio and impact response of the beam are obtained by using a Range–Kutta method and discussed in details.

Non-linear stability analysis of CNT reinforced composite cylindrical shell panel subjected to thermomechanical loading

The present study explores the nonlinear stability characteristics of simply supported carbon nanotubes (CNTs) reinforced composite (CNTRC) cylindrical shell panel subjected to combined axial compressive loading and localized heating using semi-analytical approach. The thermomechanical properties of CNTRC panel are considered to be temperature-dependent and are evaluated using extended rule of mixture method. Higher order shear deformation theory and von Kármán type nonlinearity are employed to model the CNTRC cylindrical panel. Two types of localized heating profiles such as rectangular and circular are considered along with full heating. The pre-buckling stresses generated because of applied localized heating are determined using Airy’s stress function by satisfying the strain compatibility relations. The governing equations for stability problem of CNTRC panel are derived using variational principle incorporating the obtained pre-buckling stresses. The partial differential equations obtained are converted to a set of nonlinear algebraic equations by employing the Galerkin’s technique. The buckling temperature and nonlinear equilibrium paths are determined by solving the abovementioned equations using appropriate methods. The obtained results using present semi-analytical approach demonstrated the influence of various dispersion profiles of CNTs, CNT volume fraction and heating profiles on the buckling and post-buckling characteristics of CNTRC cylindrical shell panel subjected to thermomechanical loadings.

Modelling of Thin CNTs Nanoliquid Film Flow Over a Bi-directional Stretching Surface

Unsteady flow of water and ethylene-glycol based carbon nanotubes (CNTs) nanoliquid film is examined on a bi-directional stretching surface under influence of transverse magnetic field and thermal radiation. Single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) are considered within the base liquid for investigation. Guiding full Navier–Stokes and energy equations were simplified using the thin film approximations and solved using the method of the asymptotic expansion. The result shows that nanoliquid thinning rate diminishes with rising values of CNTs volume fraction, Hartmann number and Biot number. The result also indicates that the thinning rate is more for MWCNTs with reference to the SWCNTs. It is seen that film thinning rate enhances for water-MWCNTs nanoliquid but reverse scenario is found for ethylene-glycol MWCNTs nanoliquid. The effect of various physical parameters on temperature profile has been discussed.

Static and free vibration analysis of functionally graded CNT reinforced composite plates using trigonometric shear deformation theory

In the present study, static and free vibration analysis of single walled functionally graded carbon nano-tube (CNTs) reinforced composite plate is carried out in the framework of trigonometric shear deformation theory. Trigonometric shear deformation theory full fills the traction free boundary condition at the top and bottom of the plate due to which it does not require shear correction factor. The Hamilton’s principle is used to derive governing differential equations and the Navier’s solution technique is used to obtain closed-form solution. The analytical approach is used to analyse the effect of the different span thickness ratios, volume fraction of CNTs, and distribution of CNTs on the deflection, stresses, natural frequencies, and corresponding mode shapes of CNTs reinforced composite plate. Four different types of CNTs reinforcement distribution such as, uniformly distribution (UD) and three types of functionally graded (FG) i.e. FG-O, FG-X and FG-V are selected here for the analysis. Here, the efforts are made to achieve the best possible arrangement for the reinforcement distribution that will produce the improved static and free vibration responses for the functionally graded CNTs reinforced composite plate.

Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments

This paper studies the parametric instability of hybrid nanocomposite plates under an arbitrary periodic load in thermal environments. The hybrid nanocomposite plate is a three-layer board. It has metal layers on both surfaces and one core reinforced with functionally graded (FG) carbon nanotubes (CNTs). The Galerkin method with a reduced eigenfunction transformation is applied to establish the governing equations of motion. According to the Bolotin method, a set of Mathieu-type differential equations is formed to determine dynamic instability regions and dynamic instability index (DII). The in-plane periodic stress is taken to be a combination of pulsating axial and bending stresses in the example problems. The effects of the layer thickness ratio, CNTs volume fraction, CNTs distribution type, temperature, bending stress, static and dynamic load on the dynamic instability of hybrid nanocomposite plates are investigated and discussed.

Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular physical domain into a square computational domain using the geometric transformation formulation via discrete singular convolution (DSC). The discretization of these equations is obtained via two-different regularized kernel, i.e., regularized Shannon’s delta (RSD) and Lagrange-delta sequence (LDS) kernels in conjunctions with the discrete singular convolution numerical integration. Convergence and accuracy of the present DSC transformation are verified via existing literature results for different cases. Detailed numerical solutions are performed, and obtained parametric results are presented to show the effects of carbon nanotube (CNT) volume fraction, CNT distribution pattern, geometry of skew and quadrilateral plate, lamination layup, skew and corner angle, thickness-to-length ratio on the vibration, and buckling analyses of FG-CNTR-laminated composite non-rectangular plates with different boundary conditions. Some detailed results related to critical buckling and frequency of FG-CNTR non-rectangular plates have been reported which can serve as benchmark solutions for future investigations.

Static, dynamic and natural frequency analyses of functionally graded carbon nanotube annular sector plates resting on viscoelastic foundation

In this paper, static, dynamic and natural frequency responses of composite annular sector plate with carbon nanotubes (CNTs) reinforcements resting on viscoelastic foundation are investigated. The carbon nanotubes are considered to have uniform or functionally graded pattern in the plate thickness. Kelvin-voight model is used to model the viscoelastic foundation. To model the problem, Hamilton principle based on first shear deformation plate theory and finite element method are applied. The mechanical properties of annular sector plate composed of CNTs and polymer matrix are evaluated by using the rule of mixtures. The numerical results are obtained for investigating the effect of various factors such as distribution and volume fraction of CNTs, boundary conditions, stiffness and damping coefficients of viscoelastic foundation and sector angles on natural frequency, static and dynamic transient responses of the plate.

Analysis of forced and free vibrations of composite porous core sandwich cylindrical shells and FG-CNTs reinforced face sheets resting on visco-Pasternak foundation under uniform thermal field

The radial basis function and Newmark-beta methods were used to investigate the vibrational behavior of composite sandwich cylindrical shells with porous core and functionally graded carbon nanotube. The porous core material is a kind of open-cell metal foam, whose, depending on the porosity coefficient and the core thickness, mechanical properties vary. The Hamilton principle was used to extract its motion equations. In this cylindrical sandwich shell, temperature variations are uniformly distributed and resting on the visco-Pasternak foundation with different boundary conditions. Parametric studies were presented to investigate the influence of FG porosity, temperature change, visco-Pasternak foundation, volume fraction, geometrical properties, and distribution of carbon nanotubes on natural frequencies and response dynamics of the sandwich composite cylindrical shell. The numerical outcomes express the distribution of CNTs and volume fraction play a pivotal role in the natural rates and dynamic response of the cylindrical sandwich shell. It is also perceived that there is an increase in the cylindrical shell deformation amplitude with an increase in temperature, damping, and core porosity.

Heat waves interference regarding dual-phase-lag, hyperbolic and Fourier heat conduction in CNT reinforced composites under a thermal shock

We present a framework to investigate the effects of transient heat conduction on heatwave interference and the overshooting phenomenon in carbon nanotube (CNT)-reinforced composites. Material properties of the nanocomposite are temperature and volume dependent. Different kinds of heat conduction models such as Fourier, hyperbolic or single-phase-lag (SPL), and dual-phase-lag (DPL) are considered while the media is subjected to a heat pulse or periodic thermal shock. This paper attempts to add three contributions to the existing literature: (1) using the differential quadrature method (DQM) to solve for the first time, the nonlinear DPL heat conduction equations while the materials and properties are geometry- and temperature-dependent; (2) showing the effects of the volume fraction of CNTs and their distribution on the transient heat conduction and heatwave interference; (3) demonstrating heatwave interference and the high-temperature gradient as the origins of the overshooting phenomenon. The accuracy of the present solution is confirmed by comparing it with available results from the literature.

Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation

The present study covenants with the static and free vibration behavior of nanocomposite sandwich plates reinforced by carbon nanotubes resting on Pasternak elastic foundation. Uniformly distributed (UD-CNT) and functionally graded (FG-CNT) distributions of aligned carbon nanotube are considered for two types of sandwich plates such as, the face sheet reinforced and homogeneous core and the homogeneous face sheet and reinforced core. Based on the first shear deformation theory (FSDT), the Hamilton\'s principle is employed to derive the mathematical models. The obtained solutions are numerically validated by comparison with some available cases in the literature. The elastic foundation model is assumed as one parameter Winkler - Pasternak foundation. A parametric study is conducted to study the effects of aspect ratios, foundation parameters, carbon nanotube volume fraction, types of reinforcement, core-to-face sheet thickness ratio and types of loads acting on the bending and free vibration analyses. It is explicitly shown that the (FG-CNT) face sheet reinforced sandwich plate has a high resistance against deflections compared to other types of reinforcement. It is also revealed that the reduction in the dimensionless natural frequency is most pronounced in core reinforced sandwich plate.

Nonlinear deflection analysis of CNT/magneto-electro-elastic smart shells under multi-physics loading

In this article, a first attempt has been made to address the nonlinear deflection problem of magneto-electro-elastic shells reinforced with carbon nanotubes subjected to multiphysics loads like mechanical, electric and magnetic loads. In this regard, a mathematical model based on higher-order shell theory, von-Karman’s nonlinearity is derived using finite element platform. The true flexural behavior of the functionally graded carbon nanotube reinforced magneto-electro-elastic shell under the action of individual/combined multiphysics loading is captured through higher-order nonlinear terms. Meanwhile, the results of this article emphasize on understanding the influence of coupling fields in conjunction with material and geometrical parameters on the deflection of functionally graded carbon nanotube reinforced magneto-electro-elastic shells. In addition, the study provides an intensive and meticulous insight into the deflection of curved shells with respect to different shell geometry, carbon nanotube distributions, carbon nanotube volume fractions, aspect ratio, thickness ratio, shallowness ratio, and electro-magnetic loads. The study is believed to pave way for extensive further studies on these classes of materials which can prove to be instrumental in various avenues of aerospace research and development.

A molecular dynamics investigation for predicting the effect of various parameters on the mechanical properties of carbon nanotube-reinforced aluminum nanocomposites.

Carbon nanotube (CNT)-reinforced aluminum (Al) composites are being developed to replace the conventional materials due to the enhanced stiffness for more cost-effective engineering applications. In the present study, a qualitative analysis has been conducted on carbon nanotube aluminum (CNT-Al) composites to predict the effect of CNT volume fraction, diameter, and structure (zigzag, armchair) on elastic modulus, shear modulus, bulk modulus, and ultimate tensile strength (UTS) through molecular dynamics simulation. This study shows that the elastic modulus was improved by 105% compared with pure Al, for the CNT-Al composite reinforced with the (4, 4) armchair SWCNT at a volume fraction of 8.79%. The highest value of Young's modulus of 130.37GPa occurred at the volume fraction of 11.75% for zigzag SWCNT. The CNT-Al composites showed better UTS for the Al matrix reinforced with larger diameter CNT. An enhancement of 31.65% was observed in the UTS of CNT-Al composite from 4.74 to 6.24GPa with (6, 6) CNT at 0.51% volume fraction. Elastic and bulk moduli were found to improve with a higher volume fraction of CNTs. The CNT-Al composite reinforced with smaller diameter CNT's have better elastic modulus than those reinforced with larger diameter CNT for the same volume fraction. Graphical abstract Variation of Young's modulus with SWCNT volume fraction for a constant cell size of CNT-Al composite.

Thermal effects on the free vibration of joined FG-CNTRC conical-conical shells

In this paper, the effects of temperature on free vibration of carbon nanotube reinforced composite (CNTRC) joined conical-conical shells are investigated. Carbon nanotubes (CNTs) are embedded across the thickness uniformly or functionally. Material properties of the shell are assumed to be functions of temperature. To study the free vibration of shells settled in thermal environments, it requires solving the static equations. Therefore, in order to derive these equations, first order shear deformation theory (FSDT) accompanied by von Kármán types of geometrical nonlinearity are employed in Hamilton's principle. Then, initial stress resultants due to equilibrium state, are extracted via linear membrane solution. Afterward, equations of motion are derived with regard to initial deformations and stresses. With considering the equations of motion for two cones together with boundary and continuity conditions, a set of governing equations is provided. To discretize the governing equations meridionally, generalized differential quadrature (GDQ) method is proposed. The results are primarily validated via comparing them with those of relevant researches in this field. Thereafter, some studies are carried out to exhibit the significant role of temperature variations, CNT distribution patterns, CNT volume fractions, cones' angles and boundary conditions on the free vibrational behaviors of joined conical shells. For the sake of preventing buckling occurrence during the present vibration analysis, critical buckling temperature Tcr is obtained by the procedure that the natural frequency takes zero value for the lowest temperature.

The stability of composite conical shells covered by carbon nanotube-reinforced coatings under external pressures

In this study, the stability of sandwich conical shells covered by functionally graded and uniform distributed carbon nanotube-reinforced composite coatings under external pressures is carried out. The mechanical properties of the carbon nanotube and matrix are assumed to be graded through the thickness of the coatings via three types of grading rule. The basic relationships and stability equations of sandwich conical shells reinforced by carbon nanotubes are obtained employing the modified Donnell-type shell theory and generalized first-order shear deformation theory. The Galerkin procedure is employed to define expressions for the external buckling pressures. For the accuracy of the proposed formulation, the results are compared with the results that are published in the literature. It follows a systematic study aimed at checking the sensitivity of the structural response to the type of pattern and the volume fraction of carbon nanotubes in the composite coatings.

Analytical investigation on sound transmission loss of functionally graded nanocomposite cylindrical shells reinforced by carbon nanotubes

This article presents the numerical results for acoustic transmission through relatively thick functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical shells. The vibration behavior of cylindrical shell is modeled using the first-order shear deformation theory (FSDT) which takes into account the transverse shear strains averaged over the wall thickness. Effective properties of materials of the shell reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micromechanical model based on the extended rule of mixture. Furthermore, four different types of distribution of carbon nanotubes (CNTs) along the thickness direction, i.e., UD, FG-V, FG-O, and FG-X, are considered. The shell is submerged in a fluid with an external airflow and an oblique plane wave excites on the external sidewall of the shell. In order to obtain an analytical solution of sound transmission loss (STL), the motion equations of the shell and acoustic wave equations are simultaneously solved. Then, natural frequencies and STL are extracted and they are compared with those available in the literature. Finally, the obtained results are discussed to demonstrate the effectiveness of the CNT distribution, volume fraction of CNTs, shell thickness, and Mach number on STL.

Vibration control of sandwich plate–reinforced nanocomposite face sheet and porous core integrated with sensor and actuator layers using perturbation method

In this article, the vibration control of the sandwich plate reinforced by carbon nanotube in the face sheet and porous core integrated with sensor and actuator layers is investigated. The piezoelectric layers at the bottom and top surfaces of the sandwich plate play the role of the sensor and actuator. By applying the Hamilton’s principle, the governing equations of the structure are derived based on the first-order shear deformation theory. The perturbation method is used to find the relationships between nonlinear frequency and amplitude response of the sandwich plate. The effect of porosity coefficient, temperature, volume fraction of carbon nanotube, and geometric parameters on nonlinear frequency and vibration control of the sandwich plate is studied. Moreover, the influence of material type of sensor and actuator and scale transformation parameter on the nonlinear frequency and vibration control of the system is investigated. According to the obtained results, in the case of ε < 0, the system stiffness presents softening behavior, whereas in the case of ε > 0, the system stiffness becomes hardening. By considering the effect of the voltage coefficient on the vibration control and the needed time for stabilization, the results of this article can be used to design, manufacture, and control modern structures.

Nonlinear forced vibration of sandwich plate with considering FG core and CNTs reinforced nano-composite face sheets

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

Advanced nanoindentation simulations for carbon nanotube reinforced nanocomposites

Mechanical properties of Carbon Nanotube (CNT) reinforced composites are obtained utilizing finite element (FE) method-based indentation simulations considering large strain elasto-plastic behavior of elements. This study includes nanoindentation simulations for chemically non-bonded CNT/matrix interface, including the length scale effect of nanocomposites. In order to investigate the mechanical properties of CNT reinforced nanocomposites, a number of FE models for nanoindentation tests have been simulated. Sample nanocomposites are examined to determine the suitable types of CNTs and their effectiveness as a reinforcement of different potential matrices. The Parametric study is conducted to obtain the influence of wall thickness, relative positioning, and volume fraction of CNT and strain hardening parameter of matrix on the mechanical properties of nanocomposites. The obtained results indicate that, properties such as modulus of elasticity and hardness of the nanocomposites are largely dependent on wall thickness of CNT and strain hardening parameter of the matrix. This study also suggests, the minimum wall thickness of CNT to avoid local buckling in nanocomposite which is required to be at least 0.2 nm for a diameter to thickness ratio of 5.0. Moreover, a matrix having a value of strain hardening parameter near 0.1 is expected to be significantly effective for nanocomposite.

On static bending of multilayered carbon nanotube-reinforced composite plates

In this paper, the bending behavior of single-walled carbon nanotube-reinforced composite (CNTRC) laminated plates is studied using various shear deformation plate theories. Several types of reinforcement material distributions, a uniform distribution (UD) and three functionally graded distributions (FG), are inspected. A generalized higher-order deformation plate theory is utilized to derive the field equations of the CNTRC laminated plates where an analytical technique based on Navier\'s series is utilized to solve the static problem for simply-supported boundary conditions. A detailed numerical analysis is carried out to examine the influence of carbon nanotube volume fraction, laminated composite structure, side-to-thickness, and aspect ratios on stresses and deflection of the CNTRC laminated plates.

Static performance of agglomerated CNT-reinforced porous plates bonded with piezoceramic faces

Bonding the upper and lower faces of a nanocomposite porous plate with piezoceramics eventuates a smart multidisciplinary plate (SMP). In the current work, the deflection and stress responses of such SMPs under static electrical voltages and mechanical loads have been presented. The middle plate of SMP is assumed to have simultaneous functionally graded (FG) dispersions of pore and nanofiller along the thickness. The enhancement parts of the nanocomposite material are assumed to be carbon nanotubes (CNTs) and their agglomerations with random orientations. The mechanical properties of such three-part nanocomposites are evaluated using Eshelby-Mori-Tanaka (EMT)'s technique. The coupled electromechanical governing equation of SMP under static loads is obtained by the estimation of displacement field with Reddy's third order theory (Reddy's TSDT) of plates. The coupled equation is also treated by developing a mesh-free solution to examine the impacts of embedding nanofillers and pores on the static electromechanical deflection and stress responses of SMPs. The results reveal that embedding pores up to around 90% of the volume of the middle plate leads to only 11.3% and 2.2% increase in mechanical and electrical deflections, respectively. Moreover, due to the formation of CNTs agglomerations, enhancing the middle plate with CNTs has a sharp positive impact on the reduction of deflections only up to some limited values of CNT volume fractions.