Free vibration of symmetric and sigmoid functionally graded nanobeams

Hamed, Mostafa A.; Eltaher, Mohamed A.; Sadoun, A.M.; Almitani, Khalid H.

doi:10.1007/s00339-016-0324-0

Cited by 43 publications

(12 citation statements)

References 57 publications

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“…Those investigations were carried out for bending ( [3][4][5][6][7][8][9]), buckling ( [10][11][12][13][14]) and vibration analyses ( [15][16][17][18][19][20]). The nonlocal elasticity theory was also employed to study the size-dependant behaviours of functional graded nanobeams ( [21][22][23][24][25][26][27][28][29][30][31][32][33][34]). It is well-known that the EBT underestimates deflection and overestimates buckling load and natural frequencies of thick beam due to neglecting the shear deformation effects.…”

Section: Introductionmentioning

confidence: 99%

A simple shear deformation theory for nonlocal beams

Thai

et al. 2018

Composite Structures

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In this paper, a simple beam theory accounting for shear deformation effects with one unknown is proposed for static bending and free vibration analysis of isotropic nanobeams. The sizedependent behaviour is captured by using the nonlocal differential constitutive relations of Eringen. The governing equation of the present beam theory is obtained by using equilibrium equations of elasticity theory. The present theory has strong similarities with nonlocal Euler-Bernoulli beam theory in terms of the governing equation and boundary conditions. Analytical solutions for static bending and free vibration are derived for nonlocal beams with various types of boundary conditions. Verification studies indicate that the present theory is not only more accurate than Euler-Bernoulli beam theory, but also comparable with Timoshenko beam theory.

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Section: Introductionmentioning

confidence: 99%

A simple shear deformation theory for nonlocal beams

Thai

et al. 2018

Composite Structures

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“…Aktaş and Esen [88] used FE method for vibration control of a smart beam modeled with actuator and sensor pair. Hamed et al [81] have explored the free vibration behavior of FG nanoscale beams composed of aluminum (Al) and alumina using FE method. In the study, authors have utilized Eringen's NET to give the size effect.…”

Section: Introductionmentioning

confidence: 99%

“…Al-Maliki et al [72], Aria et al [73], and Kahya and Turan [79] have used a beam FE with ten degrees of freedom in their work. According to studies of Eltaher et al [75][76][77], Aldousari [80], and Hamed et al [81], a beam FE has been analyzed with six degrees of freedom. Aria et al [74] have considered a cracked beam element with seven degrees of freedom in their work.…”

Section: Introductionmentioning

confidence: 99%

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

2023

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To the best of the authors' knowledge, this study for the first time, proposes a finite element (FE) model to investigate the size-dependent vibrational responses of guide supported imperfect functionally graded (FG) nonlocal beams embedded in an elastic foundation in the context of nonlocal elasticity theory (NET). The main objective of this paper is to present a nonlocal FE solution for vibration analysis of imperfect FG nanobeams including nonlocal effect, power-law distribution function, sigmoid distribution function, even porosity model, uneven porosity model, elastic foundation parameter, and guide support condition. It is considered that perfect/imperfect FG nanobeams are made of silicon carbide (SiC) and aluminum (Al) and that beam properties vary along the height direction. In addition, the nanobeams rest on a one-parameter elastic foundation and this foundation provides the interaction between the structure and the soil with elastic springs. The frequency values of perfect/imperfect FG power-law and sigmoid nanobeams obtained by using a nonlocal FE method are shown via tables and figures.

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“…Demir and Oz (2014) exploited the finite element method (FEM) to investigate resonance frequencies of the FG beam under viscoelastic boundary conditions. Hamed et al (2016) presented vibration characteristics of both nonlinear symmetric power and sigmoid FG nonlocal nanobeams by using the nonlocal differential Eringen's elasticity model. Frikha et al (2016) presented a 2-node, 4 degree of freedom/node beam element based on a higher-order shear deformation theory for axial-flexural-shear FGM.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

Akbaş

Bashiri

Assie

et al. 2020

Journal of Vibration and Control

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This study presents dynamic responses of a composite thick beam with a functionally graded porous layer under dynamic sine pulse load. The boundary conditions of the composite beam are considered as viscoelastic supports. Three layers are considered, and face sheet layers have porous functionally graded materials in which the distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric distribution, X distribution, and ◊ distribution). The layered composite thick beam is modeled as a two-dimensional plane stress problem. The equation of motion is obtained by Lagrange’s equations. In formation of the problem, the finite element method is used with a 12-node 2D plane element. In the solution process of the dynamic problem, a numerical time integration method of the Newmark method is used. In numerical analyses, influences of stiffness and damping coefficients of viscoelastic supports, material gradation index, porosity parameter, and porosity models on the dynamic response of thick functionally graded porous beam are investigated under the pulse load.

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Free vibration of symmetric and sigmoid functionally graded nanobeams

Cited by 43 publications

References 57 publications

A simple shear deformation theory for nonlocal beams

A simple shear deformation theory for nonlocal beams

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

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