This paper presents an efficient higher-order theory for analyzing the dynamic behavior of two types of sandwich plates: functionally graded sandwich plates (FGSPs) and four-parameter functionally graded plates (FPFGPs). The FGSP consists of two functionally graded (FG) face sheets and a ceramic core. For FGSPs, the variation follows a power-law distribution, while for FPFGPs; it adheres to Tornabene's model. To ensure that transverse shear stresses vanish at the top and bottom surfaces of the FGSP, a trigonometric shear deformation theory is employed. This theory incorporates four displacement field variables with indeterminate integral terms. The governing equations are derived using Hamilton's principle and solved using the Navier solution method for simply supported boundary conditions. Validation results demonstrate excellent agreement between the proposed theory and existing literature. Additionally, a detailed parametric study highlights the influence of key geometric and mechanical parameters, including the power-law index, side-to-thickness ratio, and aspect ratio, on the dynamic behavior of the plates.

This study investigates the free vibration analysis of a sandwich plate made of functionally graded materials (FGMs) with porosities to evaluate the natural frequency. Five parameters contribute to FGM: porous index, elastic parameters, porosity ratio, length-to-thickness ratio, and length-to-width ratio. Taking into account the thickness of the FGM plate, it is assumed that the plate has a new distribution of porosities. An investigation based on classical plate theory (CPT) examines kinematic relationships. This paper presents results for metal-ceramic functionally graded rectangular plates with a power law through the variation of volume fractions with porous ratio. A margin of error of not more than 5% applies to thin and thick plates. To validate the analytical results, a numerical investigation was conducted by employing the finite element method using ANSYS. This investigation was conducted on a 3D model of an FG system with SOLID186 an eight-noded element. Using various boundary conditions and selected models, illustrated the influence of porosity distribution characteristics on sandwich plate dynamic response. It was found that the frequency parameter of the plate increases with the increase in the sandwich structure mounting constraints. The plate thickness was divided into N layers to show the effect of several layers on the obtained results. It was found that the natural frequency for the FGM sandwich plate remains the same regardless of the number of layers for the same FGM thickness.

In this research study, the hygro-thermo-mechanical responses of simply supported porous FG sandwich plates resting on a variable elastic foundation are studied by mean of a new height order shear deformation theory. The present model satisfies the nullity conditions of the shear stresses on the upper and lower surfaces of the FG plate and without using shear correction factors. The distribution of the properties of the material through the thickness of the sandwich plate is assumed to have a distribution according to a function of the power law, while the core is assumed to be purely ceramic. The derivation of the stability equations is obtained based on the principle of virtual works. The hygro-thermal loading is considered to have a uniform, linear and non-linear variation across the thickness of the plate. To verify the accuracy of the current model, a comparison was made with other authors of the literature. The effects of the hygro-thermo-mechanical loading, the porosity, the parameters of the elastic foundation « kw and kg », the thickness ratio « a/h », the aspect ratio « a/b » and the material index « k » on the critical buckling load of the FG plate are examined.

In this paper, a refined plate theory is applied to investigate the free vibration analysis of functionally graded nanocomposite sandwich plates reinforced by randomly oriented straight carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses only four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The motion equations are derived using Hamilton's energy principle and Navier's method and is applied to solve this equation. The sandwich plates are considered simply supported and resting on a Winkler/Pasternak elastic foundation. The material properties of the functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are graded along the thickness and estimated though the Mori-Tanaka method. Effects of CNT volume fraction, geometric dimensions of sandwich plate, and elastic foundation parameters are investigated on the natural frequency of the FG-CNTRC sandwich plates.

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’ s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’ s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation.