Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

Atmane, Hassen Ait; Tounsi, Abdelouahed; Bernard, Fabrice

doi:10.1007/s10999-015-9318-x

Cited by 153 publications

(42 citation statements)

References 32 publications

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“…Atmane et al [13] investigated the effects of thickness stretching and porosity on mechanical behavior of FGM beams resting on elastic foundations. Ebrahimi and Zia [14] studied large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities.…”

mentioning

confidence: 99%

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Barati

Shahverdi

Zenkour

2016

Mechanics of Advanced Materials and Structures

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Here, free vibration analysis of functionally graded piezoelectric (FGP) plates with porosities is carried out based on refined four-unknown plate theory. The present plate theory captures shear deformation impacts needless of shear correction factor. Modified power-law model is adopted to describe the graded material properties of FG piezoelectric plate. Implementing an analytical approach which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in literature. The impacts of applied voltage, porosity distribution, material graduation, plate geometrical parameters and boundary conditions on vibration of porous FGP plate are discussed. KEYWORDS Downloaded by [University of Cambridge] at 03:23

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mentioning

confidence: 99%

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Barati

Shahverdi

Zenkour

2016

Mechanics of Advanced Materials and Structures

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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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“…Ebrahimi and Zia [56] investigated the large vibration amplitudes of porous FG Timoshenko beams by utilizing the nonlinear Galerkin and multiple scales methods. Ait Atmane et al [57] applied an efficient beam theory to study the effects of thickness stretching and porosity on the mechanical responses of FG beams resting on elastic foundations. For beams subjected to thermal environments, the first effort is due to Ebrahimi and Salari [58] who studied the vibration of porous FG Euler beams subjected to thermal loadings.…”

Section: Introductionmentioning

confidence: 99%

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Ibnorachid

Boutahar

Bikri

et al. 2019

Advances in Acoustics and Vibration

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In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

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Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

Cited by 153 publications

References 32 publications

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

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

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

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