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This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing equations of motion, which is finally solved by generalized differential quadrature method (GDQM) and perturbation method (PM). Finally, the results show that FG patterns, different orientation angle of the fiber, the VF and WCNT parameters, axial load, nonlinear temperature gradient, and applied temperature of the top surface play an essential impact on the linear and nonlinear dynamic responses of the MHCD. The more significant outcome of this research is that the effects of the VF, WCNT, θ, and β parameters on the nonlinear frequency of the MHCD can be considered at the higher value of the large deflection parameter and the effect of negative axial load on the dynamic responses of the structure is more intensive. As an applicable result show that the best functionally graded (FG) pattern for serving the highest nonlinear dynamic response of an MHC reinforced annular plate is FG-A.

This is a fundamental study on the buckling temperature and post-buckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation. The matrix material is reinforced with graphene nanoplatelets (GPLs) at the nanoscale. The displacement–strain of thermal post-buckling of the FG-GPLRC disk via third-order shear deformation theory and using Von Karman nonlinear plate theory is obtained. The equations of the model are derived from Hamilton’s principle and solved by the generalized differential quadrature method. The direct iterative approach is presented for solving the set of equations that includes highly nonlinear parameters. Finally, the results show that the radius ratio of outer to the inner (Ro/Ri), the geometrical parameter of GPLs, nonlinear elastic foundation, externally applied voltage, and piezoelectric thickness play an essential impact on the thermal post-buckling response of the piezoelectrically FG-GPLRC disk surrounded by the nonlinear elastic foundation. Another important consequence is that, when the effect of the elastic foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the thermal post-buckling of the disk and this matter is true for both boundary conditions.

In this research, we study the thermal buckling performance of multi-scale hybrid laminated nanocomposite (MHLC) disk (MHLCD) subjected hygro-mechanical loading. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macro-scale, respectively. The disk is modeled based on higher order shear deformation theory. We present a modified Halpin–Tsai model to predict the effective properties of the MHLCD. The minimum total potential energy principle is employed to establish the governing equations of the system, which is finally solved by the generalized differential quadrature method. To validate the approach, numerical results are compared with available results from the literature. Subsequently, a comprehensive parameter study is carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, moisture coefficient, stacking sequence of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio and inner radius to thickness ratio on the response of the plate. Some new results related to critical buckling of an MHLCD are also presented, which can serve as benchmark solutions for future investigations.

In this work, we study the vibration and bending response of functionally graded graphene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different substrates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element predictions performed in the commercial COMSOL code, and similar outcomes available in the literature. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the reinforcing phase, as well as the surrounding environment and boundary conditions, with very interesting insights from a scientific and design standpoint.

In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler–Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. The annular plate is modeled based on higher-order shear deformation theory (HSDT). We present a modified Halpin–Tsai model to predict the effective properties of the MHCAP. Hamilton’s principle was employed to establish the governing equations of motion, which is finally solved by the generalized differential quadrature method (GDQM). In order to validate the approach, numerical results were compared with available results from the literature. Subsequently, a comprehensive parameter study was carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, outer temperature, volume fraction and orientation angle of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio, and inner radius to thickness ratio on the response of the plate. The results show that applying a sinusoidal temperature rise and locating more CNTs in the vicinity of the bottom surface yielded the highest natural frequency.

The current paper proposes an AI-based method for the vibration control of smart plate systems. The application is set for next-generation sports engineering, where performance enhancement is the main goal. The system consists of a core of coarse aggregate ultra-high-performance concrete (CA-UHPA) and piezoelectric face sheets, which are mounted on an elastic foundation. The properties of the material composite are foreseen based on the Halpin–Tsai models and the law of mixtures. Looking into the system’s dynamic performance in a very thorough way is done using the quasi-3D theory having four variables. This theory gives the opportunity for the full consideration of the distribution of transverse shear strains and stresses throughout the plate thickness. The governing equations of the resonant response are derived by employing the concept of piezoelectricity together with Hamilton’s energy principles. The elastic foundation is analyzed using both Winkler and Pasternak coefficients, thereby allowing the interaction of the plate and its support substrate to be included. The solution is achieved through using the physics-informed neural networks (PINNs) technique, which not only accurately and efficiently replaces the conventional Legendre Polynomial Expansions with deep neural networks (DNNs) for more computational efficiency and accuracy but also doubles the legacy of AI-powered methods in terms of real-time system adaptability and optimal vibration control under changing scenarios. A DNN-based verification process assists in obtaining and confirming the trustworthiness of the results. This research marks above all and the first time as a very promising new direction in the smart systems vibration control area in sports, and it is highly anticipated that the new development will have a positive impact on the performance and durability optimization of advanced sports equipment. The introduced method embodies a patent-driven technology leap in vibration control, where AI and new materials join forces to solve challenging problems.

Honeycomb structures are one type of structure that has the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multi-scale hybrid nanocomposite (MHC) face sheets. 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 composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method. Afterward, a parametric study is carried out to investigate the effects of the thickness to length ratio of the honeycomb core, honeycomb core thickness to inner radius ratio, value fraction of carbon fibers, radius ration of the disk, the angle of honeycomb network, the weight fraction of CNTs, and tensile and compressive in-plane force on the frequency of the sandwich disk with honeycomb core and MHC. The results show that the critical fiber angle is θf/π= 0.5 for C–C and C–S boundary conditions. Another consequence is that when the structure is fixed with S–S boundary conditions, for p= 500 and p=1000, as well as the critical dimensionless angle for fibers is 0.5, there are two more range for critical fiber angle in which they are 0.275≤θf/π≤0.375 and 0.23≤θf/π≤0.39, respectively. Additionally, the range of the critical dimensionless angle for fibers increases by increasing the applied load. Some new results related to dynamic behavior of an MHC are also presented, which can serve as benchmark solutions for future investigations.

This article is the first attempt to employ deep learning to estimate the mechanical performance of multi-phase systems. Features of the design-points are obtained with the aid of the fast-converging numerical method used to solve the governing motion equations developed according to the kinematics of shear deformable structures. The optimum values of the parameters involved in the mechanism of the fully-connected neural network are determined through the momentum-based optimizer. The strength of the method applied in this survey comes from the high accuracy besides lower epochs needed to train the multi-layered network. It should be mentioned that the mechanical characteristics of the structure are computed through a two-step micromechanical scheme including the Halpin–Tsai method. The accuracy of the employed approach is examined and verified through the comparison of the results with those published in the literature. The numerical results give the practical hint that increasing the content of the reinforcement phase not always equal to increasing the resistance of the composite structure toward static instability. Thus, designers must choose the weight content of nano or macro-scale reinforcements by considering the shape factors of these materials to boost the strength of the system appropriately.

This article analyzes critical voltage and frequency information of functionally graded graphene nanoplatelets-reinforced composite (FG-GPLRC) porous cylindrical microshell embedded in piezoelectric layer, subjected to temperature gradient. The current non-classical model is capable of capturing the size dependency in the microshells by using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. To satisfy temperature boundary conditions, the Fourier series solution is extracted. In addition, for the first time, thermal conductivity coefficients regarding each GPL’s distribution pattern are presented. The thermally equations are solved via Heun’s differential equation. The mechanical properties of FG-GPLRC layer are estimated based on modified Halpin–Tsai micromechanics and rule of mixtures. Hamilton’s principle is utilized to develop governing equations of motion and boundary conditions. Finally, an analytical solution is carried out based on Navier method to obtain critical voltage and frequency in the case of simply supported shell, whereas a semi-analytical solution is proposed based on differential quadrature method (DQM) for other boundary conditions. The results show that piezoelectric layer, graphene nanoplatelets’ (GPLs) distribution pattern, porosity distribution, difference gradient thermal, length scale parameter and GPL weight function play important roles on the natural frequency and critical voltage of the GPL porous cylindrical microshell coupled with piezoelectric actuator. The results of the current study are useful suggestions for the design of materials science, micro-electromechanical systems and nano-electromechanical systems such as nano-actuators and nano-sensors.

Up to now, no studies have been yet reported to study the mechanical behaviors of three-dimensional functionally graded graphene platelets reinforced composite (FG-GPLRC) open-type panel. In this paper, the free vibration of FG-GPLRC open-type panel under multi-directional initially stressed using three-dimensional poroelasticity theory is investigated for the first time. Weight fraction of graphene open-type panel is assumed to be distributed either uniformly or functionally graded (FG) along the radial direction. Modified Halpin–Tsai model is used to compute effective Young’s modulus, whereas effective Poisson’s ratio and mass density are computed using the rule of mixture. State-space differential equations are derived from the governing equation of motion and constitutive relations in cylindrical co-ordinates. The accuracy of the obtained formulation is validated by comparing the numerical results with those reported in the available literature as well as with the finite-element modeling. The influences of several importance parameters, such as various directional initial stress, compressibility coefficient, porosity, and various type of sandwich open-type cylindrical panel, are investigated on the frequency of the structures. The results of the present study can be served as benchmarks for future mechanical analysis of cylindrical FG-GPLRC structures.