An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations

Abdelbari, Salima; Fekrar, Abdelkader; Heireche, Houari; Said, Hayat; Tounsi, Abdelouahed; Bedia, E.A. Adda

doi:10.12989/was.2016.22.3.329

Cited by 10 publications

(3 citation statements)

References 49 publications

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“…where e f is the density of reaction force of foundation. For the Pasternak foundation model [43][44][45][46][47][48][49][50][51][52][53].…”

Section: Equation Of Motionmentioning

confidence: 99%

Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium

Saidi¹,

Sahla²

2019

Frattura Ed Integrità Strutturale

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In this scientific work, a new shear deformation theory for free vibration analysis of simply supported rectangular functionally graded plate embedded in an elastic medium is presented. Due to technical problems during the fabrication, porosities can be created in side FGM plate which may lead to reduction in strength of materials. In this investigation the FGM plate are assumed to have a new distribution of porosities according to the thickness of the plate. The elastic medium is modeled as Winkler-Pasternak two parameter models to express the interaction between the FGM plate and elastic foundation. The four unknown shear deformation theory is employed to deduce the equations of motion. The Hamilton's principle is used to derive the governing equations of motion. The accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. Some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate.

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“…where e f is the density of reaction force of foundation. For the Pasternak foundation model [43][44][45][46][47][48][49][50][51][52][53].…”

Section: Equation Of Motionmentioning

confidence: 99%

Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium

Saidi¹,

Sahla²

2019

Frattura Ed Integrità Strutturale

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“…An improved simple hyperbolic shear deformation theory was introduced by Said et al (2014) to the analysis of FG plates lying on the Winkler-Pasternak elastic foundation. Abdelbari et al (2016) carried out the free vibration of FG skew plates lying on the Winkler-Pasternak elastic foundation. Ketabdari et al (2016) performed the free vibration of FG skew plates lying on the Winkler-Pasternak elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Porosity-dependent impact study of a plate with Winkler-Pasternak elastic foundations reinforced with agglomerated CNTs

Ranjbar-Roeintan

2023

AEAT

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Purpose The purpose of this article is to investigate the porosity-dependent impact study of a plate with Winkler–Pasternak elastic foundations reinforced with agglomerated carbon nanotubes (CNTs). Design/methodology/approach Based on the first-order shear deformation plate theory, the strain energy related to elastic foundations is added to system strain energy. Using separation of variables and Lagrangian generalized equations, the nonlinear and time-dependent motion equations are extracted. Findings Verification examples are fulfilled to prove the precision and effectiveness of the presented model. The impact outputs illustrate the effects of various distribution of CNTs porosity functions along the plate thickness direction, Winkler–Pasternak elastic foundations and different boundary conditions on the Hertz contact law, the plate center displacement, impactor displacement and impactor velocity. Originality/value This paper investigates the effect of Winkler–Pasternak elastic foundations on the functionally graded porous plate reinforced with agglomerated CNTs under impact loading.

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“…Functionally Graded Materials (FGMs), a new type of composite material developed in recent years, are obtained by mixing two (such as metal and ceramic) or several materials in a certain volume ratio [1]. Unlike traditional composite materials, the material composition of FGMs changes continuously along one direction without obvious delamination, so the physical properties mutation between different materials can be eliminated easily.…”

Section: Introductionmentioning

confidence: 99%

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

Huang

et al. 2020

Mathematical Problems in Engineering

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A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

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An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations

Cited by 10 publications

References 49 publications

Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium

Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium

Porosity-dependent impact study of a plate with Winkler-Pasternak elastic foundations reinforced with agglomerated CNTs

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

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