Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory

This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.

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“…Substituting Eqs. (25) and (26) into Eq. 27, one obtains the intensity of the reaction force of the foundations on the structure as:…”

Section: Assumptions Of the Present Plate Theorymentioning

confidence: 99%

“…It is also worth mentioning the existence of another model involving a second parameter; this is Pasternak's model. [23][24][25][26][27][28][29] This model takes into account the e®ect of shear interaction between adjacent points in the foundation.…”

Section: Introductionmentioning

confidence: 99%

Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

Khetib

Abbad

Elmeiche

et al. 2019

Int. J. Str. Stab. Dyn.

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“…Bellifa et al [4] applied a refined four unknowns theory to obtain the buckling behavior of FG plates. Parida and Mohanty [5] investigated FG plate buckling and free vibration response with a Winkler-Pasternak elastic base. Zenkour and Aljadani [6] reported the buckling of FG plates by considering the thickness stretching effect.…”

Section: Introductionmentioning

confidence: 99%

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

Zenkour

Aljadani

2022

Mathematics

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A quasi-3D refined theory is used to investigate the buckling response of functionally graded (FG) porous plates. The present theory takes into consideration the effect of thickness stretching. Three models of FG porous plates are presented: an isotropic FG porous plate, FG skins with a homogenous core, and an FG core with homogenous skins. The FG porous material properties vary along with the thickness of the FG layer based on modified polynomial law. By using the principle of total potential energy, the equilibrium equations are obtained. The buckling response is determined for simply supported FG porous plates. Analytical investigations are verified to present the accuracy of the current quasi-3D refined theory in predicting the buckling response of FG porous plates. The effect of thickness stretching and several parameters such as porosity coefficients, mechanical loadings, geometric parameters, gradient indexes, and layer thickness ratios are discussed. It is observed that the current theory shows more accurate results for the buckling response of FG plates compared with other shear deformation theories.

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“…11 analyzed the stochastic natural vibration of P-FG plate employing cell-based smoothed FEM with a discrete shear gap technique. Parida and Mohanty 12 used FEM to carry out the dynamic analysis and the stability analysis of P-FG plate supported on an elastic foundation. Luong et al.…”

Section: Introductionmentioning

confidence: 99%

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

Ali

Azam

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

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Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory

Cited by 21 publications

References 33 publications

Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

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