Graphene Nanoplatelets Weight Fraction Research Articles

Interfacial properties and mechanical performance of hybrid graphene/carbon fibre composites

The interaction zone between the matrix and the reinforcing component within carbon fibre (CF) composites plays a crucial role in influencing their performance characteristics, as extensively documented in scientific literature. Building on this fundamental knowledge, this research focuses to the investigation of the interface of fibrous composites and the effect of the incorporation of graphene nanoplatelets (GNPs) into the epoxy matrix. Through the utilization of laser Raman spectroscopy, a significant increase of over 60 % in interfacial strength with just a 2 % weight fraction of GNPs, as expressed by the enhanced shear-lag parameter observed in single fibre model composites, has been observed on model composites indicating a stronger interfacial interaction between the matrix and fibres. The effect of the incorporation of GNPs on CF-graphene interaction has been also investigated on a macroscopic level. Hybrid carbon fibre epoxy resin composite produced, by the introduction of GNPs into the polymer matrix. A series of mechanical tests were conducted, including extensive tensile testing of epoxy/graphene nanocomposite films, thorough examination of bending characteristics, and meticulous measurement of interlaminar shear strength for hybrid GNP/carbon fibre composites. These evaluations provided a clearer understanding of how the GNP integration affects the interface parameters that govern the mechanical behaviour of both the resin and carbon fibre composites.

Nonlinear dynamic response of FG-GPLRC beams induced by two successive moving loads

In this study, the nonlinear dynamic analysis of functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams is examined. The material properties can be estimated by using the modified Halpin-Tsai model and rule of mixture. Based on the third-order shear deformation theory and the von Kármán assumption, the equations of motion is derived and solved by using Jacobi-Ritz method incorporating with iteration procedure. Several effects such as number of layers, weight fraction of graphene nanoplatelets, material distributions, beam geometry, velocity of moving loads, distance between the loads are considered. For nonlinear forced vibration, the results indicate a considerable dissimilarity in the nonlinear dynamic deflection of the beams under moving loads when compared to linear analysis. The incorporation of additional GPLs into the beams yields a significant improvement in the strength of the beam, resulting in lower deflection. The new findings on nonlinear response of the beams excited by one and two moving loads are presented.

On characterizing the viscoelastic electromechanical responses of functionally graded graphene-reinforced piezoelectric laminated composites: Temporal programming based on a semi-analytical higher-order framework

The electromechanical responses of single and multi-layered piezoelectric functionally graded graphene-reinforced composite (FG-GRC) plates are studied based on an accurate higher-order shear deformation theory (HSDT) involving quasi-3D sinusoidal plate theory and linear piezoelectricity. These FG-GRC plates are composed of randomly oriented graphene nanoplatelets (GPLs) reinforcing fillers and the piezoelectric PVDF matrix considering two different distribution patterns such as linear- and uniform- distribution (LD and UD) of GPLs across the thickness. The modified Halpin-Tsai (HT) and Rule of mixture (ROM) models are utilized to determine the effective material properties of FG-GRCs. The analytical model of FG-GRCs is extended further to analyze the time-dependent linear viscoelastic electromechanical behavior of the system based on Biot model of viscoelasticity in the framework of inverse Fourier algorithm. The viscoelastic electromechanical responses include the static deformation and electric responses of simply supported FG-GRC plates which are investigated by considering transverse mechanical and external electrical loading, as well as other critical parameters like aspect ratio and weight fraction of GPLs. The numerical results reveal that the electromechanical response of FG-GRC plates can be enriched due to the addition of a small weight fraction of GPLs. The coupled multiphysics-based computational framework proposed here for predicting the viscoelastic electromechanical behavior of laminated composites can be exploited for stimulating and developing a wide range of micro-electro-mechanical systems (MEMS) and devices incorporating time-dependent programming features.

Machine learning based probabilistic model for free vibration analysis of functionally graded graphene nanoplatelets reinforced porous plates

In the present study, the machine learning based probabilistic model is proposed to perform the vibration analysis of functionally graded (FG) porous plates reinforced with graphene nanoplatelets (GNP). The plate is considered with the statistical variation in material properties such as elastic moduli of metal matrix and GNP, porosity index, and weight fraction of GNP while sampling via normal distribution. The effective material properties, i.e. elastic modulus and density of the GNP reinforced porous composite are respectively obtained using Halpin-Tsai and the rule of mixture models. The size and pore density are varied along the thickness direction using continuous cosine functions. The equation of motion based on higher-order shear deformable theory (HSDT) is derived using the variational principle which is further simulated by employing the finite element method (FEM) to obtain natural frequency. The database is generated based on selective input features and natural frequency i.e. output, and is further divided into 70% training dataset and 30% for testing and validation. A regression-based artificial neural network (ANN) model is adopted to learn the underlying function that maps the natural frequency to the inputs. The mapped model is further coupled with Monte Carlo simulation (MCS) to efficiently find the statistical variation in the natural frequency concerning variation in material properties (inputs) at reduced cost and time.

Free vibration analysis of functionally graded composite rectangular plates reinforced with graphene nanoplatelets (GPLs) using full layerwise finite element method

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs). Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. Therefore, it can compute interlaminar stresses and other local effects with the same accuracy as 3D FEM, requiring a lower computational cost. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young’s modulus. The rule of mixtures is applied to specify the effective Poisson’s ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine how various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio and boundary conditions of the plate, affect its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.

Mathematical modeling and vibration analysis of rotating functionally graded porous spacecraft systems reinforced by graphene nanoplatelets

This paper investigates the theoretical modeling and coupled free vibration behaviors of a rotating double‐bladed shaft assembly resting on elastic supports in a spacecraft system. According to the Kirchhoff plate theory and the Euler–Bernoulli beam theory, the theoretical model is established. The presented rotor is considered to be made of porous foam metal matrix and graphene nanoplatelet (GPL) reinforcement. Nonuniform distributions of porosity and GPLs are taken into account, which leads to the functionally graded (FG) structure. The effective material properties of the double‐bladed shaft assembly are varying along the radius and thickness directions of the shaft and blade, respectively. Moreover, the rule of mixture, the Halpin–Tsai model, and the open‐cell scheme are employed to determine its material properties. Considering the gyroscopic effect, the Lagrange equation is utilized to derive the coupled equations of motion. Then the traveling wave frequencies of the double‐bladed shaft assembly are obtained by applying the assumed modes method and substructure modal synthesis method. A detailed parametric analysis is conducted to examine the effects of the rotating speed, GPL weight fraction, GPL distribution pattern, GPL length‐to‐thickness ratio, GPL length‐to‐width ratio, porosity coefficient, porosity distribution pattern, shaft length‐to‐radius ratio, blade length‐to‐thickness ratio, support stiffness and support location on the free vibration behaviors of the double‐bladed shaft assembly.

Theoretical modeling and vibration prediction of a spinning graphene nanoplatelet reinforced cylindrical shell internal attached with a beam

This paper conducts modeling and vibration analysis of a spinning cylindrical shell attached with a beam, namely, an assembled cylindrical shell-beam structure, which is reinforced by graphene nanoplatelets (GPLs). The available performance attributes of the beam and cylindrical shell, determined by the Halpin-Tsai model together with the rule of mixture, are deemed to change continuously along their thickness directions. In accordance to the Euler-Bernoulli beam theory and the Donnell’s shell theory, the Lagrange’s equation is applied to obtain the coupled governing equations of the assembly. Besides, the substructure modal synthesis method is used to acquire vibration behaviors of the nanocomposite assembled shell-beam structure. The influences of the graphene nanoplatelet (GPL) distribution pattern, GPL weight fraction, length-to-width ratio and length-to-thickness ratio of GPLs, and spinning speed on the vibration performance of the assembled shell-beam structure. The findings could provide an important light on the design of coupled nanocomposite cylindrical shell-beam assembly for outstanding mechanical performance.

On the large amplitude vibration of shallow sandwich shells with FG-GNPRP core considering initial geometric imperfections

The present study investigates the influence of initial geometric imperfections on large amplitude vibration of shallow sandwich shells with functionally graded graphene nanoplatelets reinforced porous (FG-GNPRP) core embedded between two aluminium facets. The aluminium core is reinforced with graphene nano-platelets (GNP) and the effective properties such as elastic modulus, and mass density, etc. are estimated using Halpin-Tsai and Voigt models, respectively. The continuous functions are adopted to accomplish micro-structural gradation while creating pores which imparts the variation in material properties along thickness direction. The nonlinear governing equations based on higher order shear deformation theory and Sander’s approximation are derived using variational approach. The nonlinearity is introduced in von-Kármán sense and various imperfection modes such as sine, global and local types are considered in transverse direction. The nonlinear results are accessed using finite element method in conjunction with direct iterative technique. The influence of porosity, GNP weight fraction, imperfection amplitude, thickness, side, and radius ratios on the vibration response of the sandwich shells is explored in detail.

Vibration analysis of spinning porous cylindrical shell coupled with multiple plates assembly structures reinforced by graphene nanoplatelets

Spinning thin-walled drum coupled with multiple blades assembly structures are commonly used in modern rotor systems, where the blade and drum could be established by elastic plate model and cylindrical shell model in theory, respectively. This paper conducted theoretical modelling and vibration analysis of a spinning drum (cylindrical shell) coupled with four blades (plates) assembly. To improve its mechanical performance, this rotor system is considered to be made up of foamed metal matrix and graphene nanoplatelet (GPL) reinforcement. Graphene nanoplatelets (GPLs) are dispersed into the matrix along the thickness directions of the cylindrical shell and plates. And both uniform and non-uniform distributions of GPLs and porosity coefficients are taken into account in this paper. The substructure modal synthesis method with various interfaces is adopted to establish the coupled model of multiple plates-cylindrical shell assembly. By employing the Lagrange’s equation and the assumption mode method, the equations of motion are derived. The presented theoretical model and the obtained free vibration results are validated by the finite element method. A comprehensive discussion is carried out to examine the effects of the spinning speed, GPL distribution pattern, GPL weight fraction, length-to-thickness ratio and length-to-width ratio of GPLs, porosity distribution pattern, and porosity coefficient on the vibration behaviours of the multiple plates-cylindrical shell assembly.

Prediction of nth-order derivatives for vibration responses of a sandwich shell composed of a magnetorheological core and composite face layers

Since their mechanical qualities may be adjusted by an applied magnetic field, designers have shown considerable interest in Magneto-Rheological (MR) materials, a recently discovered class of smart materials. For the first time, this research details the vibration stability related to a sandwich shell composed of an MR core and graphene nanoplatelets (GPLs) reinforced composite (GPLRC) face layers. Residual stresses under in-plane loading contribute to the geometric stiffness considered here. This paper uses a mixed and improved Halpin-Tsai hypothesis to characterize the effective material features of GPLRC face layers. Based on the linear viscoelastic scheme and Hamilton's principle, the governing equations related to the present assembly are established. As an added bonus, compatibility equations are included to aid in providing an accurate model of the sandwich. The linked structure's governing equations under a variety of boundary conditions are solved using the wave propagation technique (WPA). Here, the authors focus on validating a Deep Neural Network (DNN) strategy for different kinds of Mean Squared Error (MSE). In conclusion, the outputs illustrate that the GPL weight fraction, viscoelastic foundation, and form of the structure are crucial in establishing the vibration stability and loss parameter factor related to the sandwich shells.

Nonlinear Bending of Sandwich Plates with Graphene Nanoplatelets Reinforced Porous Composite Core under Various Loads and Boundary Conditions

The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through the center, linear eccentric loads, uniform loads, and trapezoidal loads, has been presented. The popular four-unknown refined theory accounting for the thickness stretching effects has been employed to model the mechanics of the sandwich plates. The governing equations have been derived from the nonlinear Von Karman strain–displacement relationship and principle of virtual work with subsequent solution by employing the classical finite element method in combination with the Newton downhill method. The convergence of the numerical results has been checked. The accuracy and efficiency of the theory have been confirmed by comparing the obtained results with those available in the literature. Furthermore, a parametric study has been carried out to analyze the effects of load type, boundary conditions, porosity coefficient, GPLs weight fraction, GPLs geometry, and concentrated load radius on the nonlinear central bending deflections of the sandwich plates. In addition, the numerical results reveal that the adopted higher order theory can significantly improve the simulation of the transverse deflection in the thickness direction.

Vibration–impact study on the functionally graded graphene nanoplatelets reinforced composite curved open-type shell

This paper investigates the stability of the curved system reinforced by graphene nanoplatelets (GPLs) under low-velocity impact. Hertz contact theory is employed in order to model the contact force between the shell and the impactor. In order to acquire the displacement domains, higher-order shear deformation theory (HSDT) with twelve parameters is used. The governing equations, in addition to end conditions, are attained by the Minimum potential energy method. Then the formulations are solved through the Galerkin method as well as the Newmark method. By coupling Galerkin and Newmark methods, we solved the governing equations of the curved system under external excitation for attaining the dynamic and low-velocity impact responses. The results section shows the influence of boundary conditions, velocity, mass, and radius of the impactor, and the weight fraction of GPLs on indenter velocity, contact force, and the indentation of the GPLs reinforced open-type shell under low-velocity impact.

Free and Forced Vibration Analyses of Functionally Graded Graphene-Nanoplatelet-Reinforced Beams Based on the Finite Element Method.

The finite element method (FEM) is used to investigate the free and forced vibration characteristics of functionally graded graphene-nanoplatelet-reinforced composite (FG-GPLRC) beams. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary continuously along the beam thickness according to a linear, parabolic, or uniform pattern. For the FG-GPLRC beam, the modified Halpin–Tsai micromechanics model is used to calculate the effective Young’s modulus, and the rule of mixture is used to determine the effective Poisson’s ratio and mass density. Based on the principle of virtual work under the assumptions of the Euler–Bernoulli beam theory, finite element formulations are derived to analyze the free and forced vibration characteristics of FG-GPLRC beams. A two-node beam element with six degrees of freedom is adopted to discretize the beam, and the corresponding stiffness matrix and mass matrix containing information on the variation of material properties can be derived. On this basis, the natural frequencies and the response amplitudes under external forces are calculated by the FEM. The performance of the proposed FEM is assessed, with some numerical results obtained by layering method and available in published literature. The comparison results show that the proposed FEM is capable of analyzing an FG-GPLRC beam. A detailed parametric investigation is carried out to study the effects of GPL weight fraction, distribution pattern, and dimensions on the free and forced vibration responses of the beam. Numerical results show that the above-mentioned effects play an important role with respect to the vibration behaviors of the beam.

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

Nonlinear Transient Dynamics of Graphene Nanoplatelets Reinforced Pipes Conveying Fluid under Blast Loads and Thermal Environment

This work aims at investigating the nonlinear transient response of fluid-conveying pipes made of graphene nanoplatelet (GPL)-reinforced composite (GPLRC) under blast loads and in a thermal environment. A modified Halpin–Tsai model is used to approximate the effective Young’s modulus of the GPLRC pipes conveying fluid; the mass density and Poisson’s ratio are determined by using the Voigt model. A slender Euler–Bernoulli beam is considered for modeling the pipes conveying fluid. The vibration control equation of the GPLRC pipes conveying fluid under blast loads is obtained by using Hamilton’s principle. A set of second-order ordinary differential equations are obtained by using the second-order Galerkin discrete method and are solved by using the adaptive Runge–Kutta method. Numerical experiments show that GPL distribution and temperature; GPL weight fraction; pipe length-to-thickness ratio; flow velocity; and blast load parameters have important effects on the nonlinear transient response of the GPLRC pipes conveying fluid. The numerical results also show that due to the fluid–structure interaction, the vibration amplitudes of the GPLRC pipes conveying fluid decay after the impact of blast loads.

Nonlinear vibration of third-order shear deformable FG-GPLRC beams under time-dependent forces: Gram–Schmidt–Ritz method

This study presents nonlinear vibration of functionally graded-graphene platelet-reinforced composite (FG-GPLRC) beams under various time-dependent forces. Their material distributions are characterized by continuous functions with four patterns of reinforcement which are uniform, linear and parabolic I and II. The third-order shear deformation theory is used to represent the displacement fields, while the geometric nonlinearity is based on the von Kármán assumption. The Gram–Schmidt–Ritz method is utilized with iteration process to obtain the linear and nonlinear results. Several effects such as weight fraction of graphene nanoplatelets, types of material distributions, beam geometry, etc. on nonlinear dynamic deflection of the beams are investigated. It is found that the beams reinforced by graphene nanoplatelets mostly near the top and bottom faces are stronger than those with other different patterns of reinforcement. The comparison between the responses of continuous and multi-layers FG-GPLRC beams is presented. Some new results of FG-GPLRC beams are given and discussed in details and they can be considered as a benchmark solution for future investigations.

Dynamic characteristics of composite micro lattice plates comprises of graphene nanoplatelets based on MCST theory

This paper investigates the free vibration characteristics of a stiffened micro lattice plate with the graphene nanoplatelets (GPLs) using the modified couple stress theory and sinusoidal shear deformation theory. The governing equations of motion are derived using the Hamilton’s principle. Solution procedure is developed based on Navier’s technique for simply-supported boundary conditions. The effect of geometrical parameters of the lattice structures and GPL weight fraction on the vibration response of the functionally graded (FG) micro lattice plates is analyzed. The numerical study reveals that by increasing the cell density, the natural frequency of the FG micro lattice plate approaches to the simple FG micro plate. Also, the effect of the size, distribution pattern of GPLs and material length scale parameter on the free vibration response of the FG GPLs-reinforced micro lattice plate is demonstrated in this study.

Active Flutter Suppression and Aeroelastic Response of Functionally Graded Multilayer Graphene Nanoplatelet Reinforced Plates with Piezoelectric Patch

This paper investigates the aeroelastic flutter and vibration reduction of functionally graded (FG) multilayer graphene nanoplatelets (GPLs) reinforced composite plates with piezoelectric patch subjected to supersonic flow. Activated by the control voltage, the piezoelectric patch can generate the active mass and active stiffness that can accordingly increase the base plate’s stiffness and mass. As a result, it changes the GPLs reinforced plate’s dynamic characteristics. The motion equation of the plate-piezoelectric system is derived through the Hamilton principle. Based on the modified Halpin–Tsai model, the effects of graphene nanoplatelets weight fraction and distribution pattern on the dynamic behaviors of the plate are numerically studied in detail. The result illustrates that adding a few amounts of grapheme nanoplatelets can effectually enhance the aeroelastic properties of the plates. Two kinds of control strategies, including the displacement and acceleration feedback control, are applied to suppress the occurrence of the flutter of the plate. It shows that the displacement and acceleration feedback control can improve the critical flutter Mach number of the plate by attaching active stiffness and active mass, respectively. Furthermore, the combined displacement and acceleration feedback control has a better control effect than that of considering only one of them.

Transient response of GPLs reinforced FG-porous skewed plates subjected to blast loading

The present study investigates the transient response of graphene nanoplatelets (GPLs) reinforced functionally graded (FG) porous skewed plates subjected to blast loading. The plates are assumed to be made of Aluminium which is reinforced with graphene nanoplatelets. The effective elastic modulus and density of reinforced plates are determined by Halpin-Tsai and Voigt models, respectively. The pores are embedded throughout the volume of the plates employing symmetric and asymmetric distributions followed by certain functions. The fundamental equations are developed employing Euler-Lagrange’s equation in the framework of C0-continuous higher-order shear deformation theory. The numerical results are accessed using the finite element method and the Newmark technique is adopted to achieve a transient response of the above-mentioned plates. The influence of parameters such as porosity coefficient, GPLs weight fraction, and skew angle on the transient response of the GPLs reinforced FG-porous plates with all edges clamped and simply supported boundary conditions is demonstrated.

On linear and nonlinear bending of functionally graded graphene nanoplatelet reinforced composite beams using Gram-Schmidt-Ritz method

The current study examined the linear and nonlinear bending results of functionally graded graphene nanoplatelet reinforced composite beams. The equation system was constructed using Reddy's third order shear deformation theory and a von Kármán type nonlinear strain-displacement relationship. The nonlinear bending results of this system were solved using the Gram-Schmidt-Ritz method in conjunction with the direct iteration technique. By employing the Gram-Schmidt orthogonalization procedure for generating shape functions in the method, numerically stable functions for nonlinear bending analysis of beams were obtained. Our solutions were validated for accuracy by comparing them to some published results. The numerical results indicate that the geometrical nonlinearity of beams subjected to uniform distributed load is greater than that of beams subjected to sinusoidal, linear, or parabolic distributed loads. New results on several significant effects of reinforcement patterns, graphene nanoplatelet weight fraction, and different types of distributed loads are presented and discussed in this study, in which the findings can serve as a benchmark for future research.