GPL-reinforced Composite Research Articles

An exact analytical method for free vibration analysis of FG-GPLRC sector cylindrical shells under Levy-type boundary conditions

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.

Exploratory Study on the Application of Graphene Platelet-Reinforced Composite to Wind Turbine Blade.

With the growth of the wind energy market and the increase in the size of wind turbines, the demand for advanced composite materials with high strength and low density for wind turbine blades has become imperative. Graphene platelets (GPLs) stand out as highly premising reinforcements due to their exceptional physical properties, resulting in their widespread adoption in the composite industry in recent years. The present study aims to analyze the applicability of a graphene-platelet-reinforced composite (GPLRC) to wind turbine blades in terms of structural performance. A finite element blade model is constructed by referring to the National Renewable Energy Laboratory (NREL) 5 MW wind turbine, and its reliability is verified through a convergence test. The performance of the wind turbine blade is quantitatively examined in terms of the deflection and stress, natural frequencies, and twist angle. The applicability of the GPL-reinforced wind blade is explored through a comparison with wind blades manufactured with glass fiber and carbon nanotubes (CNTs). The comparison indicates that the performance of a wind blade can be remarkably improved by reinforcing with GPLs instead of traditional fillers, and the weight of not only the wind blade itself but also the wind turbine system can be remarkably reduced. The present results can be useful in the development of next-generation high-strength lightweight wind turbine blades.

Vibration Analysis of Perovskite Solar Cells Resting on Porous Nanocomposite Substrate in Thermal Environment

The free vibration analysis of a perovskite solar cell (PSC) within thermal environments is studied through a quasi-3D plate model. This model is designed to account for the stretching effects and non-uniform shear strains throughout the thickness. The PSC film is represented in the model as a thin laminated plate, comprising five distinct plies: ITO, PEDOT:PSS, perovskite, PCBM, and Au. A graphene platelets reinforced composite (GPLRC) substrate, made of Poly (methyl methacrylate), is assumed to be located under the noted five layers. The GPLRC substrate is conceptualized in the model as a porous foundation with finite depth. The foundation stiffnesses are determined using a modified Vlasov model, and the equivalent Young modulus of the foundation is evaluated using a modified Halpin–Tsai model, introducing the porosity coefficient. It is also considered that the material properties of GPLRC substrates exhibit temperature dependency. For the PSC with all edges simply supported, Navier solution method is applied to obtain the frequencies and associated mode numbers. Based on the results presented in this study, an increase in the porosity and thickness of the substrate can negatively impact the frequencies of the structure. However, natural frequencies experience almost no change if the temperature rises.

Free vibration and static analysis of sandwich composite plate with auxetic core and GPLRC facing sheets in hygrothermal environment

The main objective of this study is to investigate the vibration and static analysis of a sandwich composite plate in the hygrothermal environment. The plate consists of three layers such as an Aluminum auxetic core and Graphene platelet-reinforced composite (GPLRC) facing sheets. Based on the Halpin-Tsai theory and Gibson's model, the macro mechanical properties of facing sheets and auxetic core are derived. Via Reddy's third-order shear deformation theory (TSDT), the equations of motion of the sandwich plate are obtained and solved by both Navier and the generalized differential quadrature method (GDQM). The current formulation is validated by comparing the numerical results with those that are reported in the literature. Finally, the influence of different parameters such as the inclined angle of auxetic cells, thickness to the length, and core to total thickness on the natural frequencies, deflection and stresses of the sandwich plate, is examined. Even though some studies have been conducted to investigate the bending or vibration behavior of sandwich structures with negative Poisson's ratio (NPR) cores, the bending and vibration behavior of such structures in the hygrothermal environment is remained unexplored. Additionally, the analysis of stress component variations along the thickness of the plate was a novel feature that has not been addressed in prior studies on the similar structure.

Nonlinear size-dependent aerodynamics of axially reinforced doubly curved micropanel with GPLs: Application of innovative artificial neural network model

Recent years have seen significant research on oscillations in aircraft structures. A self-excited oscillation known as flutter is known to wear down aircraft equipment. So, in this work, the graphene nanoplatelets reinforced composite (GPLRC) micropanel’s nonlinear aerodynamics are modeled in this paper, and the nonlinear aerodynamics properties are validated using an artificial neural network technique. The axial direction and the material characteristics of the current system are graded. The relationship between the input layers of composite weight fraction, mode number, and slenderness ratio and the output layer of nonlinear vibrations derived from mathematical simulation has been estimated using an artificial neural network model. As a training algorithm, Levenberg–Marquardt back-propagation is employed. This study is new in that it attempts for the first time to estimate the nonlinear vibration properties of micropanels built of axially graded GPLRC material using the aforementioned input layer. Without the need to solve any differential equations or go through time-consuming experimental procedures, the suggested artificial neural network model can forecast linear or nonlinear natural frequencies. The findings demonstrate that axially graded GPLRC micropanel linear/nonlinear vibration problems can be effectively addressed using artificial intelligence techniques. Future vibration analyses of the microstructures for engineering reasons can use the provided mode.

Thermal buckling and postbuckling of functionally graded multilayer GPL-reinforced composite beams on nonlinear elastic foundations

Under the influence of axial forces and uniform temperature variations, the thermal buckling and postbuckling of composite beams reinforced of functionally graded multilayer graphene platelets (GPLs) resting on nonlinear elastic foundations are examined. The Halpin-Tsai model is used to calculate the elastic modulus of each layer of GPL-reinforced composite (GPLRC). According to the virtual work principle, the nonlinear governing equations for the beam are obtained from the first-order shear deformation beam theory. The impact of axial force and nonlinear elastic foundation on thermal buckling and postbuckling is discussed using the differential quadrature method (DQM), and the analytical expression is given by the two-step perturbation method (TSPM). The effects of axial force, boundary conditions, slenderness ratio, GPL geometry, GPL weight fraction, GPL distribution pattern, and elastic foundation coefficient on thermal buckling and postbuckling are examined through parameter analysis.

Reexamination for linear and nonlinear free vibration of porous sandwich cylindrical shells reinforced by graphene platelets

This paper reexamines the linear and nonlinear free vibration responses of porous sandwich cylindrical shells with graphene platelet (GPL) reinforcements surrounded by an elastic medium under temperature conditions. The graphene platelets reinforced composite (GPLRC) core is assumed to be multilayers, and each layer may have different values of porosity coefficient to achieve a piece-wise functionally graded pattern. By introducing an inhomogeneous model instead of the equivalent isotropic model (EIM), the Young’s moduli along with the shear modulus of porous GPLRC core are predicted through a generic Halpin–Tsai model in which the porosity is included. Thermo-mechanical properties of porous GPLRC core and metal face sheets are assumed to be temperature dependent. Motion equations of porous sandwich cylindrical shells reinforced by GPLs are formulated based on the Reddy’s third order shear deformation theory. In the modeling, von Kármán nonlinear strain-displacement relationships, shell-foundation interaction and thermal effect are also taken into account. The analytical solution for the nonlinear vibration problem is obtained by applying a two-step perturbation approach. Numerical studies are performed to compare the results obtained from the present model and the EIM. The results reveal that, in most cases, the difference of the fundamental frequency between the two models is over 10% and in that case the EIM is not suitable for the linear free vibration analysis of porous sandwich cylindrical shells reinforced by GPLs, whereas for the nonlinear-to-linear frequency ratio curves, the difference between the two models is less than 2% when the non-dimensional vibration amplitude reaches 1.0 and in that case the EIM may be valid in the analysis for the same shell.

Modeling and Re‐Examination of Nonlinear Vibration and Nonlinear Bending of Sandwich Plates with Porous FG‐GPLRC Core

In this article, an inhomogeneous model is proposed to predict the material properties of porous GPL‐reinforced composite (GPLRC) and to predict the mechanical responses of a sandwich plate which consists of top and bottom metal face sheets and a porous GPLRC core. The GPLRC core is assumed to be multilayers, and each layer may have different values of porosity coefficient to achieve a piece‐wise functionally graded pattern. Young's moduli along with shear modulus of porous GPLRC core are predicted by a generic Halpin‐Tsai model in which the porosity is included. Thermo‐mechanical properties of both metal face sheets and porous GPLRC core are assumed to be temperature‐dependent. The governing equations of motion for porous sandwich plates are solved by applying a two‐step perturbation approach to obtain the analytical solutions for the two cases of nonlinear vibration and nonlinear bending of porous sandwich plates. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results reveal that, for most cases, the difference of natural frequencies between two models is over 30%, and the vibration frequency–amplitude curves and the bending load–deflection curves are underestimated by using the EIM.

Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets

Abstract This article re-examines the nonlinear vibration and nonlinear bending responses of porous sandwich cylindrical panels reinforced by graphene platelets resting on elastic foundations in thermal environments. The graphene platelet-reinforced composite (GPLRC) core is assumed to be of multilayers, and each layer may have different porosity coefficient values to achieve a piece-wise functionally graded pattern. By introducing an inhomogeneous model instead of the equivalent isotropic model (EIM), the Young’s moduli along with the shear modulus of the porous GPLRC core are predicted through a generic Halpin–Tsai model in which the porosity is included. The thermomechanical properties of metal face sheets and the porous GPLRC core are assumed to be temperature-dependent. Governing equations of motion for sandwich cylindrical panels with porous GPLRC core are formulated based on Reddy’s third-order shear deformation theory coupled with von Kármán nonlinear strain–displacement relationships. In the modeling, the panel–foundation interaction and the thermal effects are also considered. The analytical solutions for the nonlinear vibration and nonlinear bending problems are obtained by applying a two-step perturbation approach. Numerical studies are performed to compare the results obtained from the present model and the EIM. The results confirm that the EIM is not suitable for linear free vibration analysis of sandwich cylindrical panels with the porous GPLRC core, but the EIM may be valid for the cases of nonlinear vibration and nonlinear bending analyses of the same panel resting on Pasternak elastic foundations.

Re-examination of thermo-mechanical buckling and postbuckling responses of sandwich plates with porous FG-GPLRC core

The current study re-examines compressive postbuckling and thermal postbuckling responses of porous sandwich plates resting on an elastic foundation. The core of the sandwich plates is made of porous graphene platelets reinforced composite (GPLRC). Compressive postbuckling of the porous sandwich plates under uniaxial compression at elevated temperature and thermal postbuckling of the same plates under uniform thermal loading are studied. The GPLRC core is made of multilayers, and each layer may have different values of porosity coefficient to obtain a piecewise functionally graded (FG) pattern. The Young’s moduli along with the shear modulus of the porous GPLRC core are estimated through a generic Halpin–Tsai model in which the porous nature of the material is taken into consideration. The material properties of the metal face sheets and the porous GPLRC core are assumed to be temperature dependent. The governing equations for the postbuckling of the porous sandwich plates reinforced by GPLs are established based on the Reddy’s third order shear deformation theory (TSDT). In the modeling, we also consider the von Kármán nonlinear strain–displacement relationships, the plate-foundation interaction and the thermal effect. A two-step perturbation approach is utilized in solving the postbuckling problem. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results confirm that the EIM is not suitable for analyzing buckling and postbuckling of porous plates.

Nonlinear dynamics analysis of a graphene laminated composite plate based on an extended Rayleigh–Ritz method

Linear and nonlinear vibration characteristics of the graphene platelet-reinforced composite (GPLRC) laminated plates are investigated. Based on the first-order shear theory and von Karman geometric nonlinearity, the energy expressions of the GPLRC laminates are established. The boundary elastic potential energy is established by penalty function method to simulate different boundary conditions. The linear and nonlinear frequencies of the GPLRC laminated plate are calculated by introducing boundary potential energy into Rayleigh–Ritz method. The convergence and accuracy of the method are verified by numerical examples, and the effects of different parameters on frequency are analyzed. Considering the cantilever boundary conditions, the nonlinear motion governing equations of the GPLRC laminated plate are obtained by Hamilton principle. The two-degree-freedom ordinary differential motion equations of the laminates are derived by Galerkin method. Considering the fundamental parameter resonance and 1:1 internal resonance, the amplitude–frequency response curves of the structure under transverse excitation are obtained. The effects of transverse excitation and damping coefficient on nonlinear vibration characteristics of the GPLRC laminated plates are investigated by numerical simulation.

Nonlinear free and forced vibration analysis of the sandwich composite cylindrical panel with auxetic core and GPL-reinforced facing sheets subjected to the temperature gradient

This study deals with the nonlinear free and forced vibration of a sandwich panel, composed of Graphene platelet-reinforced composite (GPLRC) skins and re- entrant auxetic core subjected to heat conduction and harmonic force excitation. The nonlinear equations are obtained by applying Hamilton’s principles in the framework’s higher-order shear deformation theory and von-Karman’s nonlinear theory. Linear and nonlinear equations of motion are solved by applying the differential quadrature method and homotopy perturbation technique, respectively. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of auxetic core, force excitation, GPL volume fraction, different boundary conditions and temperature gradient on the nonlinear frequencies- amplitude of sandwich panel are studied. Finally, the important findings of this research indicate that the ratio of core thickness, inclined angle, and thickness to inclined length have significant effects on nonlinear frequencies’ amplitude response.

Symmetric and asymmetric vibrations of rotating GPLRC annular plate

The present paper discusses the symmetric and asymmetric free and forced vibrations of a rotating graphene-platelets-reinforced composite annular plate subjected to the complex external excitation in thermal environment, where the aerodynamic force is considered. Displacement components are able to vary along the radial and circumferential directions and von Kármán’s geometrical nonlinearity is taken into account. The free vibration analysis is conducted first. Then the forced vibration equations are discretized by utilizing the Galerkin method with the aid of vibration mode. The incremental harmonic balance method and pseudo-arclength continuation algorithm are employed in combination to solve these equations. The effects of plate dimensions, graphene-platelets-reinforced composite (GPLRC) parameters, temperature rise, rotational motion, and external excitation on the symmetric and asymmetric vibration are studied by the parameter analysis for annular plate. Results implicate that temperature rise would affect the order in which the symmetric and asymmetric vibrations appear whereas the other factors not. Asymmetrical material properties along the thickness direction leads to that the periodic motion is asymmetric with respect to mid-plane. Under the complex external excitation, the dominant role of deformation shifts from symmetric vibration to asymmetric vibration as the frequency increases.

A Size-Dependent Finite Element Method for the 3D Free Vibration Analysis of Functionally Graded Graphene Platelets-Reinforced Composite Cylindrical Microshells Based on the Consistent Couple Stress Theory

Within a framework of the consistent couple stress theory (CCST), a size-dependent finite element method (FEM) is developed. The three-dimensional (3D) free vibration characteristics of simply-supported, functionally graded (FG) graphene platelets (GPLs)-reinforced composite (GPLRC) cylindrical microshells are analyzed. In the formulation, the microshells are artificially divided into numerous finite microlayers. Fourier functions and Hermitian C2 polynomials are used to interpolate the in-surface and out-of-surface variations in the displacement components induced in each microlayer. As a result, the second-order derivative continuity conditions for the displacement components at each nodal surface are satisfied. Five distribution patterns of GPLs varying in the thickness direction are considered, including uniform distribution (UD) and FG A-type, O-type, V-type, and X-type distributions. The accuracy and convergence of the CCST-based FEM are validated by comparing the solutions it produces with the exact and approximate 3D solutions for FG cylindrical macroshells reported in the literature, for which the material length scale parameter is set at zero. Numerical results show that by increasing the weight fraction of GPLs by 1%, the natural frequency of FG-GPLRC cylindrical microshells can be increased to more than twice that of the homogeneous cylindrical microshells. In addition, the effects of the material length scale parameter, the GPL distribution patterns, and the length-to-thickness ratio of GPLs on natural frequencies of the FG-GPLRC cylindrical microshells are significant.

Size-dependent nonlinear vibration analysis of cracked graphene-platelets-reinforced-composites (GPLRC) plate under parametric excitation

The response of a size-dependent randomly distributed graphene-platelet-reinforced-composite (GPLRC) plates, with an inclined part-through surface crack, resting on viscoelastic foundation under the action of periodic parametric excitation with quadratic and cubic nonlinearities are studied in the present study. The crack is centrally located at the center of the plate while inclined at an angle β concerning the X-axis. The angled crack’s mathematical formulation is based on a line-spring model. Indeed, the assumption of the problem is considered as the crack remains a continuous straight line. Nonlinearity is considered based on Berger’s formulation and Von-Karman’s geometric relations. Using classical plate theory, Eringen’s theory, micromechanical models, and equilibrium equation, the governing equation of motion of the problem have been derived. Then the Galerkin method was applied to transform the partial differential equation into the ordinary one. Eventually, the solution procedure of the cubic–quadratic nonlinear equation was followed by the multiple-scale perturbation method. Steady-state response and nonlinear softening or hardening treatment of the problem have been presented. Significant results of the study can be emphasized as GPLs, crack’s dimension and inclination, nonlocal parameter, damping, and detuning parameter effects on nonlinear behavior and stability of the structure. Dispersing GPLs as reinforcement material in the plate layer caused improvement in structural behavior, as the amplitude response of the system with the presence of a crack is decreased, comparing to a similar system without any reinforcement and crack. In the end, current work will help in the development of nonlinear behavior, stability analysis and critical bifurcation points of size-dependent cracked GPLRC plate exposed to external parametric loading.

Free vibration analysis of cylindrical sandwich panel with electro-rheological core and FG-GPLRC facing sheets based on First order shear deformation theory referred by Qatu

In this study, free vibration and damping behavior of cylindrical sandwich panel with electro-rheological core and graphene platelets reinforced composite (GPLRC) facing sheets based on first-order shear deformation theory of thick cylindrical shells referred by Qatu (FSDTQ) is investigated. Effective material properties of graphene platelets reinforced composite are determined according to the Halpin–Tsai micromechanical model. The governing equations of motion with required boundary conditions are derived using Hamilton’s principle. Afterward, these equations are solved analytically using the Fourier series solution for simply-supported boundary conditions, and for the other edges boundary conditions, we used the generalized differential quadrature method. The exactness and correctness of the present formulation are validated by comparing the results with those of existing literature. Finally, the influences of various parameters such as the electric fields, geometrically parameters, boundary conditions, the volume fraction of GPL, and GPL distributions pattern on vibration behavior and modal loss factor is examined. According to the results, the influence of the GPL volume fraction and electric field on the frequencies and modal loss factor is significant. This achievement can help design intelligent controlling structures for various applications.

Damped vibration analysis of graphene nanoplatelet reinforced dielectric membrane using Taylor series expansion and differential quadrature methods

Membrane has been attracting extensive attention due to their application in various engineering fields. Compared to traditional materials, graphene reinforced composites have demonstrated great potential in developing high-performance and multifunctional membrane structures. It is of great importance to investigate the structural behaviors of such composite membrane with considering damping and their significantly improved dielectric properties. This work studies the damped vibration of graphene nanoplatelets reinforced composite (GNPRC) dielectric membrane. Governing equations are established for the nonlinear damped vibration of the GNPRC dielectric membrane, in which the effects of dielectric properties and damping are incorporated in terms of energy. Taylor series expansion (TSE), differential quadrature (DQ) and direct iterative methods are used to numerically solve the governing equations. The model and the results are validated by comparing present results with previously reported ones. Parametric study is conducted to investigate the effects of the attributes of the electrical field and the GNP fillers, dielectric properties of the composites, damping and the stretching ratio on the nonlinear damped vibration. The result shows that the vibration frequency of the membrane can be actively tuned by changing the attributes of the applied electrical field. When the stretching ratio increases from 1.05 to 1.10, the nonlinear damped frequency can increase by 39.8%, indicating the significant effects of the stretching ratio.

An Analytical Symplectic Method for Buckling of Ring-Stiffened Graphene Platelet-Reinforced Composite Cylindrical Shells Subjected to Hydrostatic Pressure

In this paper, a novel analytical approach for the buckling of ring-stiffened porous graphene platelet-reinforced composite cylindrical shells under hydrostatic pressure is proposed under the framework of symplectic mechanics. Three types of graphene platelet-reinforced patterns and porosity distributions are considered, and the effective material properties of porous graphene platelet-reinforced composite are determined with a modified Halpin–Tsai model. In the symplectic approach, the governing equations in the conventional Lagrangian system are transformed into a set of Hamiltonian canonical equations, and therefore, the buckling analysis is reduced into an eigenproblem in a symplectic space. Consequently, the accurate critical pressures and corresponding analytical buckling mode shapes are obtained simultaneously without any trial function. The numerical results are compared with the existing results, and good agreements are observed. A comprehensive parametric study of the geometrical parameters, boundary conditions, material properties, and ring-stiffener parameters on the buckling behavior of such shells is also presented.

Nonlinear vibration characteristic of a sandwich cylindrical panel with auxetic core and GPLRC facing sheets embedded with piezoelectric layers

This paper deals with the nonlinear vibration behavior of sandwich panels composed of Graphene platelet reinforced composite (GPLRC) skins and auxetic core embedded with piezoelectric layers subjected to the thermo-magneto-electric loading. The nonlinear equations are obtained by applying Hamilton’s principles in the framework of higher-order shear deformation theory (HSDT) and von Karman’s nonlinear theory. Linear and nonlinear equations of motion are solved by applying the differential quadrature method (DQM) and homotopy perturbation technique, respectively. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of auxetic core, applied voltage, magnetic potential, GPL volume fraction, different boundary conditions, and temperature rise on the nonlinear frequency response of sandwich panel are studied. From numerical results, it was concluded that the sandwich panel incorporating auxetic core and piezoelectric layers could increase the magneto-electrical power output.

Nonlinear dynamic and forced vibration characteristic analysis of sandwich panel with double-U auxetic core and GPLRC facing sheets embedded with piezoelectric layers

The aim of the present research is to investigate the nonlinear dynamic and forced vibration of a composite sandwich panel embedded with piezoelectric layers under thermo-harmonic loading. The panel consists of a double-U auxetic honeycomb core made of aluminum alloy and graphene platelet reinforced composite (GPLRC) skins at the top and bottom surfaces. According to Gibson’s formula, the effective material properties of facing sheets and double-V auxetic core are considered. The nonlinear equations are obtained by applying Hamilton’s principles via von Karman’s nonlinear theory and higher-order shear deformation theory (HSDT). The governing equations of motion are solved by employing the differential quadrature method (DQM) and homotopy perturbation method, respectively. The accuracy of the current results has been verified by comparison with others in the literature. Finally, the influence of different parameters such as applied voltage, magnetic potential, temperature rise, different boundary conditions, and geometric parameters of core on the nonlinear frequency-amplitude response of cylindrical panels are analyzed. The numerical results show negative effect of temperature increment, positive influence of ratio of thickness to inclined length, core thickness, amplitudes of segments, considerable effect of the magnetic potential as well as small effect of applied voltage on the nonlinear vibration of sandwich panel. Finally, the important findings of this research indicate that the magnetic potential, amplitude segment, and length to inclined cell rib length have significant effects on nonlinear dynamic deflection and frequencies-amplitude response. Based on the results of this article, designers can develop different parts of aircraft.