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In this paper, the free vibration of a sandwich plate with an anisogrid core and two face sheets reinforced with graphene platelets (GPLs) is investigated. A continuous approach is considered for the lattice core and the equivalent properties are calculated. Adopting the Halpin–Tsai micromechanics, the effective Young’s modulus of the nanocomposites/graphene platelets is extracted. Also, mass density and Poisson’s ratio are earned with the simple rule of mixtures. A quasi-3D theory is applied to model the kinematics of the sandwich plate with simply supported boundary conditions. Hamilton’s principle is implemented to obtain the equations of motion that are solved based on the Navier solution. The validity of the results of this study is confirmed by comparing the analytical results with those presented in other researches and also a finite element model. The effect of the parameters of the lattice core such as the width of ribs, the number of helical ribs in one direction, and the ratio of thickness of face sheets to core on the natural frequencies of the sandwich plate was investigated. Additionally, the impact of the pattern of graphene platelets and their weight fraction on the natural frequencies were investigated. The results show that by decreasing the ratio of the thickness of face sheets to the thickness of core and increasing the number of ribs and their width, the natural frequencies will decrease. Moreover, the patterns FG-V and FG-A have the highest and the lowest natural frequencies, respectively, among the other distribution of graphene platelets.

This research aims to explore the free vibration behavior of functionally graded porous (FGP) plates resting on a Kerr-type elastic foundation. This investigation employs an innovative trigonometric shear deformation (ITSD) theory with five variables. The study encompasses various plate configurations, including homogeneous FGP plates, hard-core FGP sandwich plates, and soft-core FGP sandwich plates with both regular and irregular pore structures. The ITSD theory naturally addresses shear stress concerns at the outer surfaces, while also considering the thickness stretching effect, all without the need for correction factors. To formulate the governing equations for the free vibration of such plates on an elastic foundation, Hamilton’s principle is employed. The Navier double trigonometric series approach is then utilized to solve this problem. To validate the plate theory and methodologies used in this work, a comparative analysis is conducted with existing studies. Additionally, comprehensive parametric simulations are employed to examine the impact of different factors, such as geometric properties, material characteristics, sandwich schemes, and parameters of the Kerr-type foundation, on the dimensionless natural frequencies of simply supported rectangular FGP plates.

Metallic sandwich plates are lightweight structural materials with load-bearing and multi-functional characteristics. Previous analytic studies have shown that the bendability of these plates increases as the thickness decreases. Due to difficulty in the manufacture of thin sandwich plates, dimpled cores (structures called egg-box cores) are employed as a sandwich core. High-precision dimpled cores are easily fabricated in a sectional forming process. The cores are then bonded with skin sheets by multi-point resistance welding. The bending characteristics of simply supported plates were observed by the defining measure, including the radius ratio of the small dimple, the thickness of a sandwich plate, and the pattern angle (0°/90°, 45°). Experimental results revealed that sandwich plates with a thickness of 2.2 mm and a pattern angle of 0°/90° showed good bendability as the punch stroke under a collapse load was longer than other cases. In addition, the gap between attachment points was found to be an important parameter for the improvement of the bendability. Finally, sandwich plates with dimpled cores were bent with a radius of curvature of 330 mm for the sheet thickness of 2.2 mm using an incremental bending apparatus.

This paper investigates the free vibration of functionally graded material (FGM) sandwich plates supported by different boundary conditions and influenced by a three-parameter viscoelastic foundation and hygro-thermal changes. Three types of FGM sandwich plates are studied and discussed, in which the FGM layers vary according to the power law rule and consist of ceramic and metal materials. An efficient and simple four-variable integral higher-order shear deformation theory (HSDT) is employed to model the analytical solution of the considered problem. Hamilton principle is implemented to obtain the plates’ governing equations and to derive the eigenvalue equation for the free vibration study. The model is verified by comparing numerical results with previous studies on the vibration of exponentially graded plates. New results are presented in this paper showing the influences of different boundary conditions, hygro-thermal changes, viscoelastic parameters, vibration modes, material exponents, and geometric dimensions.

A thermomechanical bending analysis for a simply supported, rectangular, functionally graded material sandwich plate subjected to a transverse mechanical load and a through-the-thickness thermal load is presented using the refined sinusoidal shear deformation plate theory. The present shear deformation theory includes the effect of both shear and normal deformations and it is simplified by enforcing traction-free boundary conditions at the plate faces. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The equilibrium equations of different sandwich plates are given based on various plate theories. A number of examples are solved to illustrate the numerical results concern thermo-mechanical bending response of functionally graded rectangular sandwich plates. The influences played by transversal shear and normal deformations, plate aspect ratio, side-to-thickness ratio, volume fraction distributions, and thermal and mechanical loads are investigated.

This paper proposes several normalized and non-normalized displacement fields based on hybrid and trigonometric hyperbolic shear strain shape functions in order to solve the analytical thermoelastic problem of simply-supported laminated composite and sandwich plates using the Carrera unified formulation (CUF) as strategy. The equivalent single layer (ESL) governing equations for laminated composite plate are obtained by employing the principle of virtual displacement (PVD) and are solved using Navier’s method solution. Linear and nonlinear temperature distributions through the plate thickness are taken into account. A hybrid and trigonometric hyperbolic shear strain shape functions are introduced in normalized and non-normalized form in the mathematical model. The obtained results are compared with the classical polynomial ones for several order of expansion. Interesting approximations with 3D solution are shown for low and high order of expansion.

This paper is provided to study the supersonic flutter behavior of sandwich plates with a magnetorheological (MR) core and polymeric face sheets reinforced with graphene nanoplatelets (GNPs). The mathematical modelings of the plate and the aerodynamic pressure of the fluid flow are performed utilizing the first-order shear deformation theory (FSDT) and the linear piston theory, respectively. The effective mechanical properties of the face sheets are estimated utilizing the rule of mixture along with the Halpin–Tsai model. Hamilton’s principle is employed to derive the governing equations and associated boundary conditions and these equations are solved using a semi-analytical approach for a Levy-type plate. The influences of different parameters on the aeroelastic stability of the plate are investigated such as the thickness of the MR core, magnetic field intensity, distribution pattern and mass fraction of the GNPs, boundary conditions, and geometrical parameters of the plate. This paper is the first theoretical attempt to study the effects of MR materials on the aeroelastic stability of Levy-type moderately thick sandwich plates and presents useful results that will be useful in the future of air vehicles.

In this paper, an isogeometric analysis (IGA) framework based on the high-order sandwich plate theory is developed for the first time to deal with both buckling and wrinkling problems of variable-stiffness sandwich plates under compression. The present sandwich plate model is formulated based on the extended high-order sandwich plate theory (EHSAPT). The weak-form governing equations are firstly derived from the principle of virtual work, and afterward the IGA formulations based on the Non-Uniform Rational B-Splines (NURBS) are applied to predict the instability loads and the corresponding instability modes. Both the membrane and non-membrane conditions are integrated into the linear buckling analysis. The novelty of this work lies in that the employment of high-order continuous NURBS basis functions can directly fulfill the $C^1$ continuity requirement inherent in the EHSAPT theory, which enables the EHSAPT-based IGA model to be formulated with fewer degrees of freedom. Besides, the developed EHSAPT-based IGA model has also the ability to capture the overall buckling or wrinkling modes of the sandwich plates. The accuracy and effectiveness of the proposed EHSAPT-based IGA model are verified by comparison with previously published results and those obtained using ABAQUS. Effects of the core thickness and fiber angle on the buckling behaviors of the sandwich plates are also studied in numerical examples. It is observed that the non-uniform in-plane pre-stress over the skin layers is the main reason for the non-periodic wrinkling of constant-stiffness sandwich constructions, whereas the non-uniformity of both the in-plane pre-stress and out-of-plane bending stiffness is responsible for the non-periodic wrinkling of variable-stiffness sandwich constructions. The results presented herein may be beneficial for the design of variable-stiffness sandwich constructions under compression.

Analytical formulations using two higher order displacement models have been developed and solutions obtained for the first time to the natural frequency analysis of a simply supported composite and sandwich plates. These computational models are based on Taylor's series expansion of the displacements in the thickness coordinate and consider the realistic parabolic distribution of transverse shear strains through the laminate thickness. One of them considers the effects of both transverse shear and normal strain/stress while the other include only the effect of transverse shear deformation. In addition to above, few higher order and first order models developed by other investigators and already reported in the literature are also considered for evaluation. A simply supported square plate is considered throughout as a test problem. The equations of motion are obtained using Hamilton's principle. Analytical solutions are obtained using Navier's solution technique and by solving the eigenvalue problem. Firstly natural frequencies results using the various models are presented for symmetric composite plates and compared with the three-dimensional elasticity results available in the literature to show the accuracy of the higher order refined models considered in the present study in predicting the dynamic behaviour of laminated composite plates. After establishing the accuracy, natural frequencies results both at fundamental and higher modes using all the models are presented for a multilayer sandwich plates which will serve as benchmark solutions for future investigations.

Metallic sandwich plates are lightweight structural materials with load-bearing and multi-functional characteristics. Previous analytic studies have shown that the bendability of these plates increases as the thickness decreases. Due to difficulty in the manufacture of thin sandwich plates, dimpled cores (structures called egg-box cores) are employed as a sandwich core. High-precision dimpled cores are easily fabricated in a sectional forming process. The cores are then bonded with skin sheets by multi-point resistance welding. The bending characteristics of simply supported plates were observed by the defining measure, including the radius ratio of the small dimple, the thickness of a sandwich plate, and the pattern angle (0°/90°, 45°). Experimental results revealed that sandwich plates with a thickness of 2.2 mm and a pattern angle of 0°/90° showed good bendability as the punch stroke under a collapse load was longer than other cases. In addition, the gap between attachment points was found to be an important parameter for the improvement of the bendability. Finally, sandwich plates with dimpled cores were bent with a radius of curvature of 330 mm for the sheet thickness of 2.2 mm using an incremental bending apparatus.