Free vibration of functionally graded sandwich plates using four-variable refined plate theory (original) (raw)
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Journal of Sandwich Structures & Materials, 2017
In this paper, the geometrically nonlinear formulation based on von Karman’s assumptions is employed to study the large amplitude free vibrations of functionally graded materials sandwich plates. The functionally graded material sandwich plate is made up of two layers of power-law functionally graded material face sheet and one layer of ceramic homogeneous core. A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange’s equations. Employing the harmonic balance method, the equations of motion are converted from time domain to frequency domain and then solved iteratively using the linearized updated mode method. Results for linear and nonlinear frequency parameters of the simply supported functionally graded material sandwich plates are computed and compar...
IOP Conference Series: Materials Science and Engineering, 2021
In the past few decades, due to the unique material properties of functionally graded materials (FGM's), they have been used in various engineering industries. This article aims to introduce an overview of the existing literature on the area of application, stability, and free vibration analysis of FGM structures conducted by some recent research studies and to provide a comprehensive overview of the development, application, different numerical representation of materials, demonstrating procedures and arrangement technique and solution method of FGM rectangular plate. It focuses on the influence of many parameters on natural frequencies and buckling loads, such as aspect ratio, power-law index, porosity distribution throughout the thickness of the plate, and face sheet thickness. This research also involves various analyses and numerical techniques for vibration and buckling analysis of the FGM sandwich plate. Furthermore, some important notes and suggestions are put forward for future work trails in this field. It is found that there is an exceptionally restricted path to investigate the same above analysis for the FGM sandwich plate with the porous metal dependent on various parameters such as gradient index, aspect ratio, face sheet thickness, porous factor, FGM layers thickness, and the number of layers.
Archives of Materials Science and Engineering, 2021
This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.
Journal of Sandwich Structures and Materials, 2014
In this paper, a new eight-unknown shear deformation theory is developed for bending and free vibration analysis of functionally graded plates by finite-element method. The theory based on full 12-unknown higher order shear deformation theory simultaneously satisfies zeros transverse stresses at top and bottom surfaces of FG plates. A four-node rectangular element with 16 degrees of freedom per node is used. Poisson's ratios, Young's moduli, and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as power-law functions. Results are verified with available results in the literature. Parametric studies are performed for different power-law indices, side-to-thickness ratios.
A comprehensive analysis of functionally graded sandwich plates: Part 2—Buckling and free vibration
International Journal of Solids and Structures, 2005
A two-dimensional solution is presented for bending analysis of simply supported functionally graded ceramic-metal sandwich plates. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity and PoissonÕs ratio of the faces are assumed to vary according to a powerlaw distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. We derive field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Numerical results of the sinusoidal, third-order, first-order and classical theories are presented to show the effect of material distribution on the deflections and stresses.
Meccanica, 2019
A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUS TM code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction.
Free vibration analysis of functionally graded rectangular plates via differential quadrature method
2019
In this study, free vibration of functionally graded rectangular plates for various types of boundary conditions has been presented . The properties of the plate are assumed as power- law form along the thickness direction , while poisson's ratio is kept constant. the linear vibration equations of functionally graded rectangular plates are derived based on first order shear deformation theory by using Hamilton's principles . The results are tabulated for a large range of plate aspect ratios. This appears to be the first thorough study by using Differential quadrature method and First order Shear Deformation Theory based that presents effects of boundary conditions , material , and geometrical parameters on natural frequencies of functionally graded rectangular plates . The numerical results on natural frequencies of the FG plate for combination of boundary conditions, volume fraction index, radii to thickness, and aspect ratio are presented and with existing results in the l...
Composite Structures, 2013
The novelty of this research paper lies in extending the applications of differential quadrature element method to study the vibrational behavior of functionally graded rectangular plates with local elastic supports. The effective material properties of a functionally graded plate are considered to vary continuously along the thickness direction according to a volume fraction power law distribution. Based on the different arrangements of local elastic supports, the plate is divided into the elements and the governing, boundary and compatibility equations are discretized by using the generalized differential quadrature method. By assembling the stiffness and mass matrices of the plate elements at all grid points on the entire computational domain, the natural frequencies are obtained. High accuracy and eligibility of the present method are confirmed by drawing a comparison between the present results and those of the exact and other numerical solutions, and the impact of different variables and local elastic foundation arrangements on the natural frequencies is studied.
Parametric Vibrations of Functionally Graded Sandwich Plates with Complex Forms
New Trends in Nonlinear Dynamics, 2020
Buckling behavior and parametric vibrations of sandwich plates with arbitrary forms and made of isotropic and functionally graded materials (FGM) are studied. Different types of lamination schemes were considered: a sandwich plate with FGM face sheets and isotropic (metal or ceramic) core and a plate with a FGM core and ceramics or metal on top and bottom face sheets. Effective material properties are computed according to Voigt's rule in thickness direction. To calculate mechanical characteristics for different types of lamination schemes, the analytical expressions were obtained. The formulation of the problem was carried out using the first-order shear deformation theory (FSDT) of the plate. A subcritical state of the plate was taken into account.
Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory
Chinese Journal of Aeronautics, 2011
In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with functionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.