Vibration analysis of defective graphene sheets using nonlocal elasticity theory

Namin, Seyyed Feisal Asbaghian; Pilafkan, Reza

doi:10.1016/j.physe.2017.06.014

Cited by 16 publications

(7 citation statements)

References 24 publications

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“…In this case, the boundary conditions are expressed using the Chebyshev collocation method as in Eq. (16), except that each differentiation matrix D 1 is substituted with the differentiation matrix D 2 . Eq.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Moreover, Asbaghian Namin and Pilafkan [16] investigated the free vibration of defective graphene sheets via nonlocal elasticity theory, and the first-order shear deformation was used to derive the governing equations, which were solved using a generalized differential quadrature method. It was shown that the shapes and distributions of the structural defects, the number of missing atoms, and the vacancy defect reconstruction have a noticeable effect on the natural frequencies of the graphene sheets.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Buckling Analysis of Axially Functionally Graded Tapered Nano-Beams Resting on Elastic Foundation Based on Nonlocal Elasticity Theory

Sari¹,

Al‐Kouz²,

Atieh³

2018

SV-JME

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The stability analysis of nonlocal axially functionally graded tapered beams has been investigated. Euler-Bernoulli beams at the micro-or nanoscale are modeled using Eringen's nonlocal elasticity theory. The governing equations are derived using the differential constitutive relations, and the Chebyshev collocation method is utilized to convert the differential equation of motion into a set of algebraic equations. Next, the boundary conditions are applied, and the resulting eigenvalue problem is solved to obtain the critical buckling loads. The effects of the Winkler modulus parameter, the shear modulus parameter, the breadth taper ratio, the height taper ratio, the nonlocal scale coefficient, and the boundary conditions on the critical buckling loads have been studied.

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Section: Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling Analysis of Axially Functionally Graded Tapered Nano-Beams Resting on Elastic Foundation Based on Nonlocal Elasticity Theory

Sari¹,

Al‐Kouz²,

Atieh³

2018

SV-JME

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show abstract

“…One of the simplest observations with local features is the thermal vibration at room temperature with all edges of the graphene sheet clamped, which does not require specific actuations or precise environment controls. Previous research has investigated the effect of defects on the vibrational properties of graphene via various technical approaches such as molecular dynamics (MD) simulation [ 41 – 43 ], continuum elasticity theory [ 42 , 44 , 45 ], and Monte Carlo-based finite element method [ 46 ]. The local amplitudes of thermal vibrations can be affected when surrounded by defects, because the absence of atoms changes the local boundary conditions of mini-oscillators.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning-Based Detection of Graphene Defects with Atomic Precision

Zheng

2020

Nano-Micro Lett.

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“…Moreover, Namin and Pilafkan [7] used Eringen's nonlocal theory to examine the natural vibration of defective graphene sheets. Moreover, Reddy [8] applied the nonlocal elasticity theory to analyze the bending, buckling, and vibration of various beams including the Euler-Bernoulli, Timoshenko, Reddy, and Linenson beam.…”

Section: Introductionmentioning

confidence: 99%

Transverse Vibration of Functionally Graded Tapered Double Nanobeams Resting on Elastic Foundation

2020

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The natural vibration behavior of axially functionally graded (AFG) double nanobeams is studied based on the Euler–Bernoulli beam and Eringen’s non-local elasticity theory. The double nanobeams are continuously connected by a layer of linear springs. The oscillatory differential equation of motion is established using the Hamilton’s principle and the constitutive relations. The Chebyshev spectral collocation method (CSCM) is used to transform the coupled governing differential equations of motion into algebraic equations. The discretized boundary conditions are used to modify the Chebyshev differentiation matrices, and the system of equations is put in the matrix-vector form. Then, the dimensionless transverse frequencies and the mode shapes are obtained by solving the standard eigenvalue problem. The effects of the coupling springs, Winkler stiffness, the shear stiffness parameter, the breadth and taper ratios, the small-scale parameter, and the boundary conditions on the natural transverse frequencies are carried out. Several numerical examples were conducted, and the authors believe that the results may be interesting in designing and analyzing double and multiple one-dimensional nano structures.

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Vibration analysis of defective graphene sheets using nonlocal elasticity theory

Cited by 16 publications

References 24 publications

Buckling Analysis of Axially Functionally Graded Tapered Nano-Beams Resting on Elastic Foundation Based on Nonlocal Elasticity Theory

Buckling Analysis of Axially Functionally Graded Tapered Nano-Beams Resting on Elastic Foundation Based on Nonlocal Elasticity Theory

Machine Learning-Based Detection of Graphene Defects with Atomic Precision

Transverse Vibration of Functionally Graded Tapered Double Nanobeams Resting on Elastic Foundation

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