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This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in the analysis. By employing Hamilton’s variational principle, the equations of motion are derived based on hyperbolic sine function shear deformation theory. Then, the derived equations are solved analytically using the Galerkin approach. Two types of material distribution are proposed. Higher-order nonlocal strain gradient theory is employed to capture influences of shear deformation, length scale parameter (nonlocal) and material/microstructurescale parameter (gradient). Temperature-dependent material properties are considered. The validation of the proposed mathematical model is presented. Detailed parametric analyses are carried out to highlight the effects of the carbon nanotubes (CNT) distribution pattern, the thickness stretching, the geometry of the plate/shell, the boundary conditions, the total number of layers, the length scale and the material scale parameters, on the vibrational frequencies of CNTRC laminated nanoplates and nanoshells.

A new quasi-3D higher-order shear deformation theory is introduced to investigate the static behaviour of functionally graded saturated porous (FGSP) plate resting on Pasternak’s elastic foundation for the first time. The governing equations are derived from eleven-unknowns higher-order shear deformation theory and using Biot’s poroelasticity theory taking into account transverse shear stress-free boundary conditions on the top and bottom surface of the plate. Three porosity distribution patterns of FGSP materials namely uniform, non-uniform symmetric and non-uniform asymmetric are considered. Navier’s technique is employed to obtain an analytical solution. The present results are compared with 3D and higher-order solutions available in the existing literature to validate the proposed model. Parametric studies show efficiency of proposed quasi-3D plate theory in analyzing FGSP thick plates, and exploring the effects of material, geometrical and elastic foundation parameters, as well as fluid compressibility, stretching effect on transverse displacement and stress field.

This paper presents, for the first time, an effective numerical approach based on the isogeometric analysis (IGA) and the six-variable quasi-three dimensional (3D) higher-order shear deformation theory (HSDT) to study the free vibration characteristics of functionally-graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) plates submerged in a fluid medium. The plate theory incorporates the thickness stretching and the effects of transverse shear deformation without using any shear correction factors. The velocity potential function and Bernoulli’s equation are used to derive the hydrodynamic pressure acting on the plate surface. Both horizontally and vertically immersed plate configurations are considered here in the form of inertia effects. The plates are composed of multilayer GOEAMs, with the GOri content varying through the plate’s thickness in a layer-wise manner. This design results in graded auxetic growth. The material properties are evaluated by mixing rules and a genetic programming (GP)-assisted micromechanical model. The governing equations of motion for the FG-GOEAM plates immersed in a fluid medium are derived by Hamilton’s principle. After validating the convergence and accuracy of the present model, a comprehensive parametric study is carried out to examine the effects of the GOri content, GOri distribution pattern, GOri folding degree, fluid level, immersed depth, and geometric parameter on the natural frequencies of the FG-GOEAM plates. The results show that the natural frequencies for the four GOri distribution patterns increase with the increase in the layer number when the lay number is fewer than 10, and then stabilize after the layer number reaches 10. Besides, in general, the natural frequency of the FG-GOEAM plate in a vacuum or fluid increases when the GOri content increases, while decreases when the GOri folding degree increases. Some additional findings related to the numerical results are presented in the conclusions. It is believed that the present results are useful for the precise design and optimization of FG-GOEAM plates immersed in a fluid medium.

This research addresses the three-dimensional thermomechanical wave propagation behavior in sandwich composite nanoplates with a metamaterial honeycomb core layer and double functionally graded (FG) ultra-stiff surface layers. Due to its potential for high-temperature applications, pure nickel (Ni) is preferred for the honeycomb core layer, and an Al 2 O 3 /Ni ceramic-metal matrix is preferred for the surface layers. The functional distribution of graphene platelets (GPLs) in three different patterns, Type-U, Type-X, and Type-O, in the metal-ceramic matrix with a power law distribution provides double-FG properties to the surface layers. The mechanical and thermal material characteristics of the core and surface layers, as well as the reinforcing GPLs, are temperature-dependent. The pattern of temperature variation over the plate thickness is considered to be nonlinear. The sandwich nanoplate’s motion equations are obtained by combining the sinusoidal higher-order shear deformation theory (SHSDT) with nonlocal integral elasticity and strain gradient elasticity theories. The wave equations are established by using Hamilton’s principle. Parametric simulations and graphical representations are performed to analyze the effects of honeycomb size variables, wave number, the power law index, the GPL distribution pattern, the GPL weight ratio, and the temperature rise on three-dimensional wave propagation in an ultra-stiff sandwich plate. The results of the analysis reveal that the 3D wave propagation of the sandwich nanoplate can be significantly modified or tuned depending on the desired parameters and conditions. Thus, the proposed sandwich structure is expected to provide essential contributions to radar/sonar stealth applications in air, space, and submarine vehicles in high or low-temperature environments, protection of microelectromechanical devices from high noise and vibration, soft robotics applications, and wearable health and protective equipment applications.

This paper aims to develop a nonlocal strain gradient meshfree plate approach which combines the nonlocal strain gradient theory (NSGT), higher order shear deformation theory (HSDT) and meshfree method, for the bending and free vibration analyses of laminated composite and sandwich nanoplates. Mechanical characteristics of small-scale structures can be described by using two scale parameters related to the nonlocal and strain gradient effects. The weak form of governing equations is extracted from the virtual work principle. Exploiting the higher order derivatives of moving Kriging (MK) shape functions, the present approach satisfies the requirement of the third-order derivatives of weak approximations. The displacements and natural frequencies of laminated composite and sandwich nanoplates are then determined by utilizing the MK meshfree method. Numerical results show that the deflections and natural frequencies of laminated composite and sandwich nanoplates are significantly influenced by the boundary conditions, nonlocal parameter and strain gradient parameter, geometry, length-to-thickness ratios. As observed, a large difference between NSGT and classical HSDT results is reported and discussed. It is clear that the results of both models coincide when the nonlocal and strain gradient parameters are taken as zero.

This paper investigates the geometrically nonlinear vibration characteristics of all-composite honeycomb core sandwich panels (ACHCSP). The proposed theoretical model incorporates the higher-order shear deformation theory, Gibson equivalent theory, and Von Kármán’s large deformation theory to enhance its nonlinearity. The vibration equations are derived using both the orthogonal polynomial method and the energy method, while the vibration frequencies are obtained through solving the energy function. To ensure the model’s accuracy, parameters related to nonlinearity are calibrated. Subsequently, ACHCSP experimental specimens were meticulously prepared, followed by frequency sweep and resonant excitation experiments to rigorously validate the accuracy of the proposed theoretical model. The experimental results demonstrate that the proposed theoretical model possesses a remarkable capability to accurately predict the nonlinear vibration characteristics of ACHCSP, as evidenced by a maximum discrepancy of 5.64% between the theoretical calculations and pre-experimental results. In conclusion, this study investigated the impact of varying honeycomb layer thickness, honeycomb unit wall thickness, and honeycomb unit wall length on the nonlinear vibration characteristics of ACHCSP. The obtained results offer valuable insights with significant implications for both engineering applications and academic research.

The free vibration behavior of a new advanced functionally graded (FG) nanobeam is presented in this work using the recently proposed nonlocal higher-order shear deformation theory. In the present theory, the stress tensor can satisfy the parabolic variation of the shear stress distribution throughout the thickness direction and also fulfill the requirement that the shear stress on the top and bottom surfaces of the FG nanobeam is zero. Two common types of FG structures, namely, FG hardcore and FG softcore, are considered here for analysis with three schemes. The material properties of the FG nanobeam are assumed to vary continuously in both the longitudinal and transversal directions according to a combined simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of the FG nanobeam with simply supported boundary conditions are derived using the proposed higher-order shear deformation plate theory. The nonlocal strain gradient theory is employed to capture the microstructure-dependent effect. The influence of the structural geometry, the gradient index, and the nonlocal and length scale parameters on the vibration frequency is investigated. Finally, many new results are also reported in the current study, which will serve as a benchmark for future research.

Free vibration and buckling analyses of the magneto-electro-elastic functionally graded (MEE FG) microplates in thermal environment are investigated for the first time. The MEE FG microplate is composed of two phases: piezoelectric (barium titanate) and piezomagnetic (cobalt ferrite) materials, which are distributed across the thickness direction based on the power law model. To satisfy Maxwell’s equation in the quasi-static approximation, the electric and magnetic fields are assumed a combination of trigonometric and linear functions across the plate thickness. To capture small effects on microstructures, the modified strain gradient theory (MSGT), including three length scale parameters combined with the generalized higher-order shear deformation theory (HSDT), is presented. The equilibrium equations for free vibration and buckling analyses of MEE FG microplates are derived by using Hamilton’s principle. Through those equations, the natural frequency and critical buckling load of MEE FG microplates are computed by using isogeometric analysis (IGA). Based on the Non-uniform rational B-splines (NURBs) basic functions, which achieve any desired degree of continuity of basis functions, the IGA easily satisfy the MSGT model’s higher-order derivatives. The advantage and accuracy of the proposed model are demonstrated through comparisons between the present results and those provided in the literature. The effect of the electric voltage, magnetic potential, power index, geometrical parameter and length scale parameters on the dimensionless frequencies and critical buckling loads of the MEE FG microplates is fully reported. The article’s results can be considered as benchmark solutions for the vibration and buckling of MEE FG microplates and they are helpful for manufacturing sensors, actuators, stability control, etc.

This paper presents dynamic formulation for a sandwich cylindrical panel based on higher order shear-deformation theory and Hamilton’s principle. The sandwich cylindrical panel is composed of a porous core sandwiched by two graphene origami-reinforced copper matrix layers. The material properties of porous core and graphene origami-reinforced copper matrix layers are estimated using the Halpin–Tsai and rule of mixture for various distributions of porosity and graphene origami dispersion in terms of material and geometric characteristics of constituent materials. Through calculation of strain energy, kinetic energy and external work, the governing equations of motion are derived using Hamilton’s principle. The analytical solution is applied for parametric analysis of the problem. The natural frequencies are analytically obtained in terms of material and geometric parameters of graphene origami such as volume fraction and folding degree, various distributions, porosity coefficient, porosity distribution, and temperature. The numerical results indicate that the maximum natural frequency is obtained for X distribution of graphene origami.

This paper aims to investigate the influence of material uncertainties on the postbuckling behaviour of functionally graded porous beams reinforced with graphene platelets when subjected to a thermal environment. A comprehensive deterministic, as well as stochastic study, has been done by employing the stochastic finite element methodology. The temperature-dependent (TD) and temperature-independent (TID) material properties have been considered. The homogenized effective material properties such as Young’s modulus are estimated by using the Halpin-Tsai micromechanics model and the density, and thermal expansion coefficient by Voigt’s rule of mixture. The homogenized material properties are assumed to be varying along the thickness direction in a functionally graded manner. The developed formulation is based on higher-order shear deformation theory in conjunction with Von-Kármán type geometric non-linearity for the postbuckling analysis. A C 0 finite element model is developed to solve the system of non-linear governing equations, which are solved numerically using the direct iterative procedure. The convergence and validation study of the developed formulation has also been performed with an independent Monte Carlo simulation to ensure the accuracy of the formulation. The influence of material uncertainty on the thermo-mechanical postbuckling behavior of FG-GPLRC porous beams has been discussed for low variability (randomness) in material design parameters such as porosity content, amount of nanofillers, and material properties (i.e., Young’s modulus, density of metal matrix, and nanofillers) respectively. It was revealed that uncertainties in material properties can significantly affect the postbuckling response of FG-GPLRC porous beams.