Graphene Nanoplatelets Weight Fraction Research Articles

Thermally induced instability on asymmetric buckling analysis of pinned-fixed FG-GPLRC arches

In the present work, an analytical study on the asymmetric static and dynamic buckling of a pinned-fixed functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) arch under thermal conditions is presented. The reinforcement of graphene nanoplatelets (GPLs) is dispersed along arch thickness by following a power law distribution. Making use of the modified Halpin–Tsai micromechanical model and energy method, the static buckling load of the arch under an arbitrary radial point load and the dynamic buckling load of the arch under an arbitrary radial step point load can be derived, which could be applied to determine the existence of dynamic buckling and the phenomenon of multiple limit points under a static state. A numerical analysis is conducted to verify the accuracy of the analytical method, a good prediction on the static and dynamic buckling of the pinned-fixed FG-GPLRC arch is demonstrated. In this study, the influence of GPLs weight fraction, concentration and geometry on the static and dynamic buckling of the arch is comprehensively discussed. The dynamic and static buckling loads of the arch are found to be sensitive to applied load position under various elevated temperatures. Arch buckling load decreases as the power law index increases, but it increases as temperature rises. It is also found that the present approach is able to trace the postbuckling paths of the arch for stability analysis. Besides, accurate first-known thermal buckling solutions are also presented.

Dynamic mechanical analysis of graphene nanoplatelets/glass reinforced epoxy composite

This paper presents a study on dynamic mechanical analysis (DMA) of graphene nanoplatelets (GNPs)/glass reinforced epoxy composite. The composite was fabricated by a hand lay-up technique followed by vacuum bagging technique. GNPs weight fraction was 0.5 and 1.5 wt.% for a fixed glass fibre fraction. The test was carried out in terms of storage modulus (E’), loss modulus (E”), and tan δ. The result indicates that 1.5 wt.% GNPs/glass reinforced epoxy composite obtain the maximum value of the dynamic mechanical properties due to the incorporation of GNPs nanofiller. The improved dynamic mechanical properties were related to better interfacial interaction of the nanofiller with the epoxy matrix. The glass transition temperature (Tg) value for 0.5 and 1.5 wt.% GNPs/glass were 62.84 and 66.01 °C, respectively.

Wave dispersion characteristics of graphene reinforced nanocomposite curved viscoelastic panels

This paper tries to investigate the wave phenomenon in nanoshell made of graphene nanoplatelets (GNPs) reinforced nanocomposites. The second-order shear deformation theory in curvilinear coordinate is utilized to develop the doubly-curved shell as a continuous structure and the general nonlocal strain gradient theory is adopted to calculate nonlocality and strain gradient size-dependency. The effective material properties are estimated through the Halpin–Tsai micromechanical model and a modified rule of mixture. A virtual work of Hamilton statement is employed to obtain the governing motion equations and then a harmonic solution based on an analytical procedure is developed to find the wave response. Afterwards, a parametric study is performed to analyze the effects of the linear spring and damper coefficients, small-scale parameters, different curves, radius to thickness ratio, GNP's weight fraction as well as its number of layers on the phase velocity response of the GNPs reinforced doubly curved nanoshell with various shape panels resting on a visco-Winkler medium.

Meshless numerical approach to flutter analysis of rotating pre-twisted nanocomposite blades subjected to supersonic airflow

In this study, the flutter analysis of a rotating pre-twisted functionally graded graphene nanoplatelets reinforced composite (FG GPLRC) blade under supersonic airflow is investigated. The pre-twisted blade is multi-layered and reinforced with graphene nanoplatelets (GPLs) evenly distributed in each layer while the GPL weight fraction changes from layer to layer through the thickness direction. The effective Young's modulus is determined by Halpin-Tsai micromechanical model while the Poisson's ratio and mass density are predicted by Voigt's rule for GPLRC layers. According to assumptions of the first-order shear deformation theory (FSDT), the first-order piston theory and shell theory, the dynamic model of rotating pre-twisted GPLRC blades subjected to supersonic flow is developed. Meshless the improved moving least-square Ritz method (IMLS-Ritz) is used to derive the discrete dynamic equations of rotating pre-twisted GPLRC blades under aerodynamic load. The accuracy of the IMLS-Ritz method for this problem is validated by comprehensive convergence studies and careful comparison studies. A detailed parameter investigation of the effects of GPL distribution configuration, rotation velocity and geometrical parameters on flutter behavior characteristics of GPLRC blades is systematically conducted.

Intelligent wave dispersion control of an inhomogeneous micro-shell using a proportional-derivative smart controller

The goal of the present research is an investigation of the smart control and wave propagation examination of a graphene nanoplatelets reinforced (GPLRC) cylindrical micro-shell covered with piezoelectric layers as the sensor and actuator (PLSA) in the framework of an analytical method. The stress and strain components are given based on the first-order shear deformable theory (FSDT), and for accessing the size effects, the nonlocal strain gradient theory is used for obtaining the correct results. The material properties of the GPLRC micro-shell are modeled via modified Halpin–Tsai and the rule of the mixture. The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. The governing equations of the electrically micro-shell are derived via Hamilton’s principle. This work concludes that the PD controller, wave number, applied voltage, and weight fraction of graphene nanoplatelets (GPL) have a significant influence on the wave propagation of the GPLRC cylindrical micro-shell. The remarkable result is that consideration of the PD controller leads to expand the stable area and improve the dynamic behaviors of the smart system.

Vibration Characteristics of Functionally Graded Porous Nanocomposite Blade-disk-shaft Rotor System Reinforced with Graphene Nanoplatelets

This paper presents a study on the modelling and free vibration analysis of a rotating functionally graded (FG) porous blade-disk-shaft assembly reinforced with graphene nanoplatelets (GPLs) resting on elastic supports. The rotor is made of graphene nanoplatelet (GPL) reinforced porous foam metal matrix. Both uniform and non-uniform distributions of GPLs and pores in the rotating assembly are considered. The effective material properties are thought of as layered change along the directions of blade thickness, disk radius and shaft radius. Moreover, the material values of this functionally graded structure are determined via the open-cell scheme, the Halpin–Tsai model together with the rule of mixtures. According to the finite element (FE) method, the modelling and free vibration analysis of the nanocomposite blade-disk-shaft rotor system is conducted. To verify the present analysis, the experimental method is adopted. The FE results and experimental results have great match with each other. Special attention is paid to the effects of the rotating speed, GPL distribution pattern, GPL weight fraction, length-to-width ratio and length-to-thickness ratio of GPLs, porosity distribution, porosity coefficient and support stiffness. The obtained conclusions can give particularly important suggestions for the design of GPL reinforced porous blade-disk-shaft rotor systems to achieve advanced mechanical performance.

Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets

This article deals with the frequency analysis of viscoelastic sandwich disk with graphene nano-platelets (GPLs) reinforced viscoelastic concrete (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the concrete. By employing Hamilton's principle, the governing equations of the structure are derived and solved with the aid of the Generalize Differential Quadrature Method (GDQM). In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Afterward, a parametric study is carried out to investigate the effects of the outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the concrete, the weight fraction of GPLs into concrete, and the thickness of honeycomb core to inner radius ratio on the frequency of the viscoelastic sandwich disk with honeycomb core and FGGPLRVC face sheet.

Vibration characteristics of graphene nanoplatelet reinforced disk-shaft rotor with eccentric mass

This paper presents an investigation on vibration characteristics of graphene nanoplatelet (GPL) reinforced disk-shaft rotor with eccentric mass resting on elastic supports. The shaft is made of common metal material while the disk is made of graphene nanoplatelet reinforced material. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary smoothly and continuously along the thickness direction of the disk, which leads to a functionally gradient (FG) structure. The effective properties of the disk are determined via the Halpin-Tsai micromechanics model and the rule of mixture. In accordance with the Timoshenko beam theory and Kirchhoff plate theory, the governing equations which take into account gyroscopic effect due to rotation are derived by using the Lagrange equation. The substructure modal synthesis method and the assumed modes method are utilized to obtain the natural frequencies, and the Runge-Kutta method is adopted to solve the forced vibration response of the rotor system, where the centrifugal force and gravity of an eccentric mass in the shaft are considered as generalized forces. The present analysis is validated through comparison with both experiment and finite element (FE) results. A detailed parametric study is conducted to examine the effects of the rotating speed, GPL weight fraction, GPL distribution pattern, length-to-thickness ratio and length-to-width ratio of GPLs, disk position, disk dimension, and support stiffness on vibration behaviors of the nanocomposite disk-shaft rotor system.

Modeling and free vibration analysis of rotating hub-blade assemblies reinforced with graphene nanoplatelets

This paper presents a new theoretical model for rotating elastic hub-blade assemblies, made of functionally graded (FG) graphene nanoplatelet (GPL) reinforced nanocomposites, and their free vibration characteristics are investigated. This model is the first attempt to include two elastic components simultaneously and consider the coupled effect. The Euler-Bernoulli beam theory and the Donnell’s shell theory are employed to establish the mathematic model of the blade and hub, respectively. The effective material properties, varying continuously along the thickness of the beam and cylindrical shell, are determined via the Halpin-Tsai micromechanics model and the rule of the mixture. The Lagrange’s equation is adopted to derive the equations of motion which are then solved by employing the substructure mode synthesis method and the Galerkin method. A parametric study is conducted to examine the effects of the rotating speed, graphene nanoplatelet distribution pattern, GPL weight fraction, length-to-thickness ratio and length-to-width ratio of graphene nanoplatelets (GPLs) and blade dimension on the natural frequencies of the nanocomposite rotor system, which will significantly benefit on the structural and material design of GPL reinforced hub-blade assembly.

Free vibration analysis of a spinning porous nanocomposite blade reinforced with graphene nanoplatelets

This paper investigated the modeling and free vibration characteristics of a spinning graphene nanoplatelet (GPL) reinforced porous nanocomposite blade. The blade is made of porous foam metal matrix reinforced with graphene nanoplatelets (GPLs). Several different GPL distributions and porosity distributions in the blade are taken into account. The effective material properties of the blade, determined via the open-cell scheme, the Halpin-Tsai model, and the rule of mixture, are assumed to be varying continuously along the its thickness direction. According to the Kirchhoff’s plate theory, the governing equations of the spinning blade are derived by adopting the Hamilton principle. On the other hand, the non-uniform spinning blade is modeled by the finite element method which is compared with the theoretical method. The theoretical results match very well with the finite element ones obtained from ANSYS. Particular focus is given to the effects of the spinning speed, porosity coefficient, distribution pattern of GPLs and porosities, GPL weight fraction, length-to-thickness ratio and length-to-width ratio of GPLs, blade length, and spinning radius on the free vibration performance of the blade rotor.

An accurate size-dependent sinusoidal shear deformable framework for GNP-reinforced cylindrical panels: Applications to dynamic stability analysis

In the current work, an accurate modified couple stress-based cylindrical micro-panel model is developed in the framework of sinusoidal shear deformation theory. The classical strain tensors and curvature tensor components in a modified couple stress-based model are given with consideration of the geometric curve of cylindrical panels. In conjunction with a general Lagrange procedure, the proposed model is implemented to derive a system of Mathieu-Hill equations of governing dynamic stability behaviors of the cylindrical micro-panels. The Navier-type solution and Bolotin's method are applied to predict the principle unstable regions of the micro-panels with simply-supported boundary condition. As an application of the proposed model, the size-dependent stability of a functionally graded graphene nanoplatelets reinforced composite (FG-GNPRC) cylindrical micro-panel under axial oscillation compression is investigated for the first time. It is assumed that the weight fraction of graphene nanoplatelets (GNPs) is graded in the panel thickness. The effective Young's modulus of FG-GNPRC is determined based on a modified Halpin–Tsai model, while the mixture rule used to evaluate the effective Poisson's ratio and the mass density. The parameter studies are performed to examine the effect of dimensionless length parameter, GPL distribution patterns, GPL size and shape, length-to-span ratio and radius-to-span ratio on the size-dependent dynamic stabilities of FG-GNPRC cylindrical micro-panels.

Free vibration analysis of a rotating graphene nanoplatelet reinforced pre-twist blade-disk assembly with a setting angle

This paper investigates the coupled modeling method and free vibration characteristics of a graphene nanoplatelet (GPL) reinforced blade-disk rotor system in which the blade has a pre-twist angle and setting angle. Based on the Kirchhoff plate theory and the Euler–Bernoulli beam theory, the theoretical model of the rotating blade-disk assembly is carried out accurately. The effective material properties of the blade and disk are assumed to vary continually along their thickness directions and are determined via the Halpin–Tsai micromechanics model together with the rule of mixture. The coupled equations of motion are derived in accordance with the Lagrange's equation. Then, the substructure modal synthesis method and the Galerkin method are employed to calculate the free vibration results of the rotor. Additionally, the effects of the rotating speed, GPL distribution pattern, GPL weight fraction, length-to-thickness ratio and length-to-width ratio of GPLs, inner and outer radius of the disk, and pre-twist angle per unit length, setting angle and length of the blade on free vibration characteristics of the rotating blade-shaft assembly are discussed in detail.

Analytical investigation on the nonlinear postbuckling of functionally graded porous cylindrical shells reinforced with graphene nanoplatelets

The objective of this study is an analytical investigation on the nonlinear postbuckling of functionally graded porous cylindrical shells reinforced with graphene nanoplatelets (GNPs). It is assumed that the GNP and porous distribution patterns vary smoothly through the thickness. Three distribution schemes are considered for GNP and porous media distributions. The effective material properties are calculated via a micromechanical method. By considering the geometric nonlinearity, the energy functional of the considered system under the combined axial and radial compressions is obtained based on the classical sell theory. Then, an analytical solution procedure based on the Ritz method and Airy function is used to obtain the nonlinear postbuckling behavior of considered system with simply supported boundary conditions. Finally, the effect of different parameters such as porous distribution, GNP scheme, porosity coefficient, GNP weight fraction and geometry on the nonlinear buckling loads, and postbuckling behavior is studied.

Dynamical behaviors of conveying-fluid nanocomposite toroidal shell segments with piezoelectric layer in thermal environment using the Reddy’s third-order shear deformation shell theory

Nonlinear dynamics of the conveying-fluid toroidal shell segments made of functionally graded (FG) graphene nanoplatelets (GNPs) with piezoelectric layers are investigated in this paper. The Halpin-Tsai micromechanical model is used to derive the material properties. The various distribution patterns of the shells are given as the uniform distribution (UD) and functionally graded (FG) reinforcements by modifying the volume fraction of matrix/GNPs in the thickness direction. The fluid flow in the internal shell is mentioned as non-viscous, incompressible, isentropic and irrotational. The governing equations is expressed by using the Reddy's third-order shear deformation shell theory, Von Karman-Donnell geometrical nonlinearity assumption, and combining the internal fluid-flow. Then, the dynamical characteristics of the nanocomposite shells are obtained by applying the Airy's stress function and the Galerkin's method. The calculate programs are written by codes of Wolfram-Mathematica and the obtained results are compared with the previous literatures. In addition, the effects of the thermal environment, GNPs weight fraction, GNPs distribution patterns and geometric parameters are carefully scrutinized. The results can be applied in significant applications of industries engineering as aerospace, civil and mechanical engineering.

Coupled free vibration of a functionally graded pre-twisted blade-shaft system reinforced with graphene nanoplatelets

The free vibration of a rotating functionally graded (FG) pre-twisted blade-shaft assembly reinforced with graphene nanoplatelets (GPLs) is analytically investigated based on the coupled model proposed in this paper. The effective material properties of the blade and shaft are assumed to vary continuously along their thickness and radius directions, respectively, and are determined by Halpin-Tsai micromechanics model and the rule of mixture. Within the framework of the Rayleigh beam theory and Euler-Bernoulli beam theory, the governing equations of motion are derived by using Lagrange’s equation. The substructure synthesis method and assumed modes method are utilized to determine the natural frequencies of the system. A comprehensive parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, geometry and dimensions as well as the blade length, location and pre-twist angle, the shaft length and rotating speed on the natural frequencies. The research findings shed an important light on the design of novel graphene reinforced blade-shaft system for remarkably improved dynamic performance.

Multiple Equilibria and Buckling of Functionally Graded Graphene Nanoplatelet-Reinforced Composite Arches with Pinned-Fixed End

This paper presents an analytical study on the multiple equilibria and buckling of pinned-fixed functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) arches under central point load. It is assumed that graphene nanoplatelets (GPLs) in each GPLRC layer are uniformly distributed and randomly oriented with its concentration varying layer-wise along the thickness direction. The Halpin–Tsai micromechanics-based model is used to estimate the effective elastic modulus of GPLRC. The non-linear equilibrium path and buckling load of the pinned-fixed FG-GPLRC arch are subsequently derived by employing the principle of virtual work. The effects of GPLs distribution, weight fraction, size and geometry on the buckling load are examined comprehensively. It is found that the buckling performances of FG-GPLRC arches can be significantly improved by using GPLs as reinforcing nanofillers. It is also found that the non-linear equilibrium path of the pinned-fixed FG-GPLRC arch have multiple limit points and non-linear equilibrium branches when the arch is with a special geometric parameter.

An analytical solution for vibration analysis of sandwich plates reinforced with graphene nanoplatelets

In this study, the free vibration of a composite sandwich plate reinforced with graphene nanoplatelets (GPLs) enclosed by piezoelectric layers is investigated using an analytical solution. In the framework of the first-order shear deformation plate theory, multilayer functionally graded graphene platelets-reinforced composite plate is assumed. Applying modified Halpin–Tsai model and rule of mixtures, the effective Young’s modulus, mass density and Poisson’s ratio of nanocomposites are predicted. In each individual layer, the weight fraction of GPL nanofillers illustrates a layer-wise variation along the thickness direction either uniformly or non-uniformly GPLs dispersed. Based on Maxwell’s equation, the electric potential in a piezoelectric layer is considered for open and closed circuit boundary conditions. Coupled governing equations of motion and boundary conditions are derived by using the Hamilton’s principle. Four auxiliary scalar functions are introduced to decouple the governing equations of motion and boundary conditions, which are solved analytically by employing Levy-type boundary conditions. The effects of GPLs weight fraction, GPLs distribution patterns, number of layers and aspect ratio are examined in detail. The results show that the best way to predict the most effective reinforcement is to distribute more GPLs with a larger surface area near the top and bottom surfaces of the plate. Besides, adding a small amount of GPLs as reinforcing nanofillers can significantly improve the stiffness of the plate.

Semi-numerical simulation for vibrational responses of the viscoelastic imperfect annular system with honeycomb core under residual pressure

This composition investigates the frequency analysis of sandwich imperfect viscoelastic disks with graphene nano-platelets (GPLs)-reinforced viscoelastic composite (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum because of its high stiffness and low weight. The modified Halpin-Tsai model and rule of the mixture have been utilized to provide the effective material constant of the composite layers. Through employing Hamilton's principle, the governing equations of the structure are accordingly discerned and resolved by utilizing the Generalized Differential Quadrature Method (GDQM). Throughout this investigation, viscoelastic properties have been modeled in accordance with Kelvin-Voigt viscoelasticity. The deflection as the function of time is capable of being resolved through employing the fourth-order Runge-Kutta numerical method. Afterwards, a parametric study is conducted to discern the effects of the FG patterns, outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the GPLs, the weight fraction of GPLs, FG face sheet thickness ratio, the thickness of honeycomb core to inner radius ratio, tensile, imperfect coefficient, and in-plane force on the frequency of the sandwich viscoelastic disk with honeycomb core and FG-GPLRVC face sheet.

Effects of non-uniform elastic foundation on the nonlinear vibration of nanocomposite plates in thermal environment using Selvadurai methodology

This paper focuses on effects of non-uniform elastic foundation, that impact on non-linear thermal dynamics of the simply supported plate reinforced by functionally graded (FG) graphene nanoplatelets (GNPs). The Halpin-Tsai micromechanical model and the rule of mixtures are employed to calculate the material properties. By adjusting the volume fraction of matrix/GNPs in the thickness direction, the various distribution patterns of the plates are considered as the uniform distribution (UD) and functionally graded (FG) reinforcements. The governing equations is expressed by using the classical theory, Von Karman-Donnell geometrical nonlinearity assumption, and combining the temperature change. Then the dynamical behaviors of the FG-GNPs reinforced plates are obtained by applying the Airy's stress function and the Galerkin's method. The obtained results are described by the column charts, the 2D and 3D graphs and written by codes of Wolfram-Mathematica. In addition, the present study scrutinizes the effects of the thermal environment, GNPs weight fraction, GNPs distribution patterns, damping coefficient and geometric parameters. More importantly, the influences of the longitudinal variable thickness of Pasternak’s subgrade model on the dynamical characteristics are analyzed to optimize structures. Altogether these findings have significant applications in industries engineering and lead to breakthroughs in the microstructures design.

Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets

This paper presents a robust and accurate analytical solution based on the refined higher-order shear deformation theory for establishing the buckling capacity of a series of simply-supported sandwich plates. Each sandwich plate consists of an open-cell metal foam core with various pore distributions and two metal face sheets. Cores with and without GNP-reinforcements are considered. Three different distributions of porosity are considered for the core (i.e., uniform and two different non-uniform distributions along the thickness of the core). The effective properties of the porous cores are estimated by employing the modified Halpin-Tsai micromechanical model and the rule of mixture. The governing differential equations are solved analytically using the Navier method. Subsequently, the Box-Behnken design (BBD) statistical method, which is a subset of the response surface methodology (RSM), is employed to investigate the simultaneous effect of the input variables (i.e., porosity coefficient, the core to total thickness ratio and the weight fraction of graphene nanoplatelets (GNPs)) on the buckling capacity of the sandwich plates. This is followed by the development of a set of simple and practical equations for evaluating the critical buckling capacity of the sandwich plates as a function of the input variables.