Free vibration and bending of functionally graded beams resting on elastic foundation

Akbaş, Şeref Doğuşcan

doi:10.17515/resm2015.03st0107

Cited by 27 publications

(15 citation statements)

References 19 publications

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“…Sun et al [33] numerically investigated buckling and post-buckling under thermomechanical deformations of a FG Timoshenko beam resting on a two-parameter nonlinear elastic foundation and subjected to only a temperature rise with the shooting method. Akbas [34] investigated the free vibration and static bending of FG beams resting on Winkler foundations within the Euler Bernoulli beam theory and the Timoshenko beam theory. e material properties of the beam changed in the thickness direction according to power-law distributions.…”

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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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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“…Many authors have studied the dynamic behavior of FGM beams, mostly, T by means of both the classical beam theory (CBT), FSDBT and HSDBT Wang et al [1] given a solution to solve the free vibration, buckling and bending problems of the Timoshenko and Euler-Bernoulli beams based on different models of elastic foundations. There are many areas of application for composite materials (Chikh et al [2]; Akbaş et al [3]; Chikh et al [4]; Fahsi et al [5]) same the aircraft and aerospace industry. Omidi et al [6] studied the dynamic stability of simple supported FG beams reposing on a linear elastic foundation; with piezoelectric-layers under a periodic axial compression load.…”

Section: Introductionmentioning

confidence: 99%

Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations

Chikh

2019

Frattura Ed Integrità Strutturale

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In this article, an analytical study was done to predict the behavior of the beam vis-à-vis bending, buckling, and dynamic responses of isotropic homogeneous beams based on an elastic foundation. The material properties of the FG-beams vary across the thickness using the power law. In this work, the sinusoidal shear deformation beams theory is used to investigate the static and dynamic behavior of FG beams. The present theory fulfills the condition of nullity of edge stresses and does not require the use of a shear correction factor. Hamilton's principle is used to deduce equations of motion, and analytical solutions for simply supported beams were obtained using the Navier resolution method. Nondimensional displacements, eigenfrequencies and critical-buckling loads of isotropic homogeneous beams were obtained for various values of the foundation parameters. The numerical results obtained by the present technique have been compared with the results of literature and are in excellent agreement with them. It can be concluded that the current HSDBT is simple and accurate in solving the bending, eigenfrequency and critical-buckling load problems for FGM beams.

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“…[24] fonksiyonel derecelendirilmiş elasto-manyetik konsol bir kirişin düzlem problem ile analitik olarak incelemiştir. Son yıllarda fonksiyonel derecelendirilmiş malzemelerin mekanik davranışları ile ilgili bir çok çalışma literatürde yer almıştır [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionunclassified

Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi

Akbaş¹

2017

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Free vibration and bending of functionally graded beams resting on elastic foundation

Cited by 27 publications

References 19 publications

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

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

Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations

Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi

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