An Investigation on the Characteristics of Bending, Buckling and Vibration of Nanobeams via Nonlocal Beam Theory

Benguediab, Soumia; Semmah, Abdelwahed; Chaht, Fouzia Larbi; Mouaz, Soumia; Tounsi, Abdelouahed

doi:10.1142/s0219876213500850

Cited by 12 publications

(9 citation statements)

References 31 publications

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“…This result for the zigzag nanobeam is in accordance with the predictions of the nonlocal theory, [4,59] nonlocal shear deformation theory, [11] numerical meshless method, [15] and nonlocal shear deformation of the hyperbolic theory. [12] However, for the armchair nanobeam the amount of deflection is reduced and the nanobeam is harder compared to the local case which agrees with the predictions of the gradient [31] and Eringen-like models. [31] Thus, it may be concluded that a change in chirality can have a substantial effect on the hardness and softness of nanobeams.…”

Section: Simply Supported Nanobeams (S-s)supporting

confidence: 76%

“…Table 3 illustrates for what values of length L, the scaling and chirality effects are more important. For this purpose, a normalized deflection is defined̂= 12 ∕ 0 . The classical normalized deflection is considered as the baseline and the percent variances of the deflection of zigzag and armchair Euler-Bernoulli nanobeams using Equations 60 and 61 are presented with respect to the baseline.…”

Section: Resultsmentioning

confidence: 99%

“…Unlike most of the non‐local beam theories that have only one scale parameter, one version of the non‐local theories, known as the hybrid model, includes two independent scale parameters . Other non‐local theories include non‐local shear deformation beam theory and non‐local hyperbolic shear deformation theory which do not need any shear correction factors.…”

Section: Introductionmentioning

confidence: 99%

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Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

2018

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By taking the effect of the scale parameter explicitly into account, bending behavior of Euler‐Bernoulli and Timoshenko nanobeams is studied using doublet mechanics. In addition, the effect of chirality on the softening or hardening behavior of an Euler‐Bernoulli nanobeam in bending is studied by taking the effect of the chiral angle explicitly into account. For the bending of the Timoshenko nanobeam the effect of the scale parameter and chirality on the axial and shear stresses is studied and the results are compared with the gradient and Eringen‐like models. It is shown that as the chiral angle increases, a simply supported Timoshenko nanobeam under a uniform loading changes from a softening to a hardening nanobeam indicating that chirality has a pronounced effect on the bending response of the nanobeams.

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Section: Simply Supported Nanobeams (S-s)supporting

confidence: 76%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

2018

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“…6,7 There are numerous studies related to the wave propagation, static, buckling and free linear and nonlinear vibration analysis of nanobeams and nanotubes based on di®erent beam theories. [8][9][10][11][12][13][14][15][16][17][18][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] The theory of surface elasticity established by Gurtin et al 7 has been adopted to explain various size-dependent phenomena at the nanoscale, and the predictions¯t well with atomistic simulations and experimental measurements. [19][20][21] Wang and Feng 22 analyzed the surface e®ects on the axial buckling of nanowires.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Analytical Evaluation of Surface and Nonlocal Effects on Buckling and Vibrational Characteristics of Nanotubes with Various Boundary Conditions

Ebrahimi

Shaghaghi

Boreiry

2016

Int. J. Str. Stab. Dyn.

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In the present paper, the vibrational and buckling characteristics of nanotubes with various boundary conditions are investigated considering the coupled e®ects of nonlocal elasticity and surface e®ects, including surface elasticity and surface tension. The nonlocal Eringen theory is adopted to consider the e®ect of small scale size, and the Gurtin-Murdoch model the surface e®ect. Hamilton's principle is employed to formulate the governing equation and di®erential transformation method (DTM) is utilized to obtain the natural frequency and critical buckling load of nanotubes with various boundary conditions. The results obtained match the available ones in the literature. Detailed mathematical derivations are presented and numerical investigations are performed. The emphasis is placed on the e®ects of several parameters, such as the nonlocal parameter, surface e®ect, aspect ratio, mode number and beam size, on the normalized natural frequencies and critical buckling loads of the nanotube. It is explicitly shown that the vibration and buckling of a nanotube is signi¯cantly in°uenced by these e®ects. Numerical results are presented which may serve as benchmarks for future analysis of nanotubes.

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“…Thus, based on this new model, many studies have been conducted by developing and providing nonlocal beam models for the prediction of mechanical behaviors of homogenous and nonhomogeneous nanobeams. 31–52 Zhang et al. 53 carried out a free vibration study of nonlocal Timoshenko beams made of FGMs by employing symplectic method; the influences of various parameters were presented.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

Bensaid

Daikh

Draï

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

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An Investigation on the Characteristics of Bending, Buckling and Vibration of Nanobeams via Nonlocal Beam Theory

Cited by 12 publications

References 31 publications

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

A Semi-Analytical Evaluation of Surface and Nonlocal Effects on Buckling and Vibrational Characteristics of Nanotubes with Various Boundary Conditions

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

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