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The existing study examines the moisture-dependent vibrational behavior of a metal foam spherical panel that is positioned between two composite layers reinforced with graphene platelets (GPL). The Kerr foundation, a three-parameter elastic foundation, supports the model. Based on specified functionalities, the pores’ arrangement and the GPL dispersion throughout the core and face sheets, respectively, are taken into consideration. The Halpin–Tsai and extended rule of mixture micromechanical models are utilized to ascertain the face sheets’ effective hygromechanical property values. After the motion equations are determined, the frequencies are extracted using the analytical technique, which is particularly effective for shells with simply supported edges. The impacts of various influences on the natural frequencies are considered and addressed over the course of the inquiry. It is shown that natural frequencies drop with increasing porosity coefficient. Furthermore, a small amount of GPL is shown to have a strong reinforcing effect on the stiffness of the structure, hence enhancing natural frequencies. The outcomes of this investigation can be beneficial to a variety of industries such as aerospace, automotive, marine, and civil engineering, where spherical shells are commonly employed. Furthermore, the outcomes might function as a standard for subsequent research. These results not only advance the understanding of moisture effects on composite structures but also provide a foundation for future research aimed at optimizing material properties for specific applications. Additionally, this study offers practical insights for the design and manufacturing of more resilient and efficient spherical components in real-life engineering scenarios.

Owing to the exceptional qualities of nanocomposite materials and the vast array of applications for porous lightweight structures, combining them results in structures that are both rigid and lightweight. Therefore, this work examines the buckling resistance of a porous cylindrical shell with graphene platelets reinforced composite (GPLRC) that is supported by a Pasternak substrate that can withstand normal and shear stresses and is sandwiched between two metal face sheets. Based on predetermined functionality, the configuration of the pores and the distribution of GPLs within the core are examined. The effective mechanical properties of the core of the shell are obtained by incorporating the Gaussian random field model for closed cellular solids with micromechanical models like Halpin-Tsai and the extended rule of mixture. An analytical method designed for shells with simply supported edges is used to generate critical buckling loads using equilibrium equations derived from a higher-order shear deformation theory. The study thoroughly evaluates how different factors affect the outcomes. The results showed that the largest values of critical buckling loads were obtained from the symmetric pattern of pore distribution, which outperformed the uniform and non-symmetric patterns. Critical buckling stresses also increased as the weight fraction of GPLs increased. The results have practical implications for sectors using cylindrical shells and could be used as a standard for similar studies in the future.

An analysis is done in this research on the dynamical behavior of thick sandwich plates subjected to a moving load. The considered sandwich plate is composed of a porous aluminum core augmented with graphene platelets (GPLs) and titanium alloy face sheets. The core of sandwich plate is identified as a porosity-dependent composite and consists of six layers with each of them having different values of porosity. The time-dependent equations of motion are established for the sandwich plate by implementing the principle of virtual work. The governing equations are numerically solved for different boundary conditions utilizing the Ritz technique. The Newmark time marching scheme is also applied to obtain the temporal evaluation of displacement field in the plate volume. The verification example demonstrates the effectiveness and accuracy of the applied formulation. Novel numerical examples are presented to study the influences of porosity distribution pattern and its coefficient on the dynamic characteristics of the sandwich plate. Also, the effects of graphene’s weight fraction, plate’s geometric parameters and its boundary conditions are examined.

This paper examines the free and forced vibration characteristics of metal foam nanocomposite shallow arches with two Titanium alloy layers under a moving load. The middle core is made of a six-layer porous aluminum reinforced with graphene platelets in which different dispersion distributions are taken into account. The basic governing equations in the sandwich arch under moving load are established based on the first-order shear deformation model, Halpin–Tsai modified rule and Hamilton’s principle. The equations of motion are extracted for the sandwich arch with simply-supported boundaries by applying the Fourier expansions. An eigenvalue solution is applied in the free vibration problem and the Newmark time marching scheme is used for the forced vibration problem. The computed results from this investigation are compared with those reported data in the literature. Then, novel numerical examples are presented in detail to show the influences of important effective parameters on the free and forced vibrations of shallow sandwich arches.

This paper investigates the buckling behavior of graphene platelets (GPL) reinforced composite cylindrical shells with cutouts via finite element method (FEM) simulation. Young’s modulus of the composites is determined by the modified Halpin–Tsai micromechanics model while the mass density and Poisson’s ratio of the composites are approximated by the rule of mixture. Comprehensive parametric study is conducted to investigate the effects of the weight fraction and the shape of GPL fillers, the geometry of the shell and the position and orientation of the cutout on the buckling behaviors of the cylindrical structures. The results demonstrate that the addition of GPLs can significantly increase the load bearing capacity of the cylindrical shells. Larger sized GPLs with fewer single graphene layers are favorable reinforcing fillers in enhancing the buckling performances of the structures. The buckling load is sensitive to the location of the cutout with larger aspect ratio. Moreover, the orientation of the cutout is found to have significant effects on the buckling load when the orientation angle $\theta$ is falling within the ranges – $\pi$/2 $\le \theta \le$ – $\pi$/4 and $\pi$/4 $\le \theta \le \pi$/2.

In this research, the natural frequency behavior of functionally graded (FG) porous joined hemispherical–cylindrical–hemispherical shell vessels reinforced by graphene platelet (GPLs) has been studied for the first time. Three various types of porosity distribution are assumed through the thickness direction of shell vessel. In the two types of porosity patterns, a pattern of porosities in metal matrix is symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in metal matrix. Extended role of mixture and Tsai-Halpin is used to determine the mass density and Young’s modulus of elasticity of the structure, respectively. By employing 3D elasticity theory, Hamilton’s Principal and FEM in conjunction with Rayleigh–Ritz method, the governing equations of motion of the joined shell vessel are obtained and natural frequencies are extracted. The impact of various factors such as coefficient of porosity, several porosity patterns along with different GPLs distributions and weight fraction of graphene nanofillers on natural frequency behavior of FG porous joined hemispherical–cylindrical–hemispherical shell vessels reinforced by GPLs nanofillers has been reported for the first time.

The composites reinforced by graphene and its derivatives have demonstrated great potential in developing high-performance and smart materials and structures. This paper numerically studies the dynamic characteristics of functionally graded (FG) graphene platelets (GPLs) reinforced composite (FG-GPLRC) dielectric beam subjected to damping, mechanical excitation and electrical field. Required mechanical and physical properties of the composites are evaluated by effective medium theory (EMT). Governing equations for the structure are established based on Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship. Differential quadrature (DQ) and incremental harmonic balance (IHB) together with an arc-length algorithm are combined to discretize and solve the highly nonlinear equations. The effects of the geometry and concentration of GPLs, attributes of electrical field, FG distribution profile, excitation and damping on the dynamic characteristics of the beam are comprehensively investigated. Two transition regions for the effect of AC (alternating current) frequency of the electrical field on the dynamic performances of the beam are identified. There exist thresholds for GPL concentration, FG slope factor and aspect ratio for the dynamic response of the composite beam. It is indicated that the dynamic performances of the FG composite beam can be actively tuned by changing the attributes of the electrical field. The numerical investigation is envisaged to provide guidelines for the design and optimization of developing smart engineering structures.

Buckling of a circular graphene-platelet-reinforced composite plate resting on an elastic foundation is investigated in this research for the first time. The equations governing the thermal buckling of the circular plate were derived based on Hamilton’s principle, classical theory, and the von Kármán strain field. The effective material properties were determined by the Halpin-Tsai model and the rule of mixture. The plate is divided into two sections where solution of stability equation for each section is determined exactly. Applying the boundary and continuity conditions, a transcendental equation is established which may be used to obtain the critical buckling temperature and number of nodal diameters at the onset of buckling. In the end, and after validating the results, the effects of the laminated graphene-platelet-reinforced plate configuration, elastic foundation properties and dimensions, and the graphene platelet weight fraction on the critical thermal buckling temperature were investigated.

This paper investigates the wave propagation in the graphene platelets (GPLs)-enhanced functionally graded porous plates. The governing equations of motion are obtained using the first-order shear deformation plate theory (FSDT). Subsequently, the equations are transformed into the state-space form. The wave dispersion relation is derived by solving the state space equation by means of the method of reverberation-ray matrix and the accuracy of this approach is validated through a comparative analysis with the results from relevant literature. In addition, parametric analyses are carried out, including boundary conditions, porosity coefficient, GPL mass fraction, porosity distribution, GPL distribution, and thickness-to-width ratio, on the dispersion behavior of functionally graded GPLs-reinforced porous plates. The use of GPLs in these composites is particularly promising, and the findings offer valuable insights into the design of composites with tailored properties for specific engineering applications.

In this study, the vibration of functionally graded porous truncated conical shell reinforced with graphene platelets (GPLs) is investigated. The GPLs nanofillers and pores are considered to be uniform and nonuniform throughout the thickness direction. Using Hamilton’s principle, the governing equations are derived based on Love’s first approximation theory. The generalized differential quadrature method is applied to solve the governing equations of motion and to obtain the natural frequencies of the shells for various boundary conditions. Applying the Halpin–Tsai model and the rule of mixture, the effective elastic modulus, the Poisson’s ratio and the density of nanocomposite shell reinforced with GPLs are computed. The effects of porosity coefficients, distribution patterns of porosity, GPL weight fraction, geometry and size of GPLs, semi-vertex angle as well as boundary conditions on the natural frequency of the system are analyzed. It was observed in the results that the shells with symmetric porosity distribution reinforced by graphene platelet pattern A predict the highest natural frequencies. Furthermore, it was found that the natural frequencies of nanocomposite conical shell can be decreased by increasing the porosity coefficient. Besides, the geometry and size of GPLs as well as weight fraction of GPLs have significant effects on the natural frequencies.

This is the first research on the buckling and free vibration analysis of functionally graded graphene platelets reinforced composite annular plate resting on elastic substrate and subjected to nonlinear temperature gradient and mechanical load within the framework of higher order shear deformation theory (HSDT). Governing equations and boundary conditions are established by employing Hamilton’s principle. Generalized differential quadrature method is applied to obtain numerical solution. Considering nonlinear temperature gradient instead of the linear one and also the effects of elastic substrate besides describing the kinematics on the basis of HSDT makes the results closer to real condition. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of stiffness of the substrate, patterns of temperature rise, temperature gradient, axial load, weight fraction and distribution patterns of GPLs, outer radius to inner radius ratio, inner radius to thickness ratio of the plate and geometric dimensions of GPLs on the response of the structure. This study provides essential information to engineers seeking innovative ways to promote the composite structures in a practical way.