Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory

Farajpour, Mohammad Reza; Shahidi, Alireza; Tabataba’i-Nasab, Fahimeh S.; Farajpour, Ali

doi:10.1140/epjp/i2018-12039-5

Cited by 42 publications

(21 citation statements)

References 38 publications

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“…However, stiffness hardening has been observed in some small-scale structures, especially at higher lengths. This stiffness hardening can be estimated incorporating surface effects [75][76][77][78][79][80] or strain gradients [52,53,[81][82][83][84][85][86]. For example, it was found that the pure nonlocal plate model cannot completely predict the buckling instability of circular graphene sheets subject to axisymmetric radial loading [87] by employing MD simulations.…”

Section: Nonlocal Strain Gradient Elasticitymentioning

confidence: 99%

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A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

210

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Understanding the mechanical behaviour of nanostructures is of great importance due to their applications in nanodevices such as in nanomechanical resonators, nanoscale mass sensors, electromechanical nanoactuators and nanogenerators. Due to the difficulties of performing accurate experimental measurements at nanoscales and the high computational costs associated with the molecular dynamics simulations, the continuum modelling of nanostructures has attracted a considerable amount of attention. Since size influences have a crucial role in the mechanics of structures at nanoscale levels, classical continuum-based theories have been modified to incorporate these effects. Among various modified continuum-based theories, the nonlocal elasticity and the nonlocal strain gradient elasticity have been employed to estimate the mechanical behaviour of nanostructures. In this review paper, first these two modified elasticity theories are briefly explained. Then, the nonlocal motion equations for different nanostructures including nanorods, nanorings, nanobeams, nanoplates and nanoshells are derived. Several papers which reported on the size-dependent mechanical behaviour of nanostructures using modified continuum models are reviewed. Furthermore, important results reported on the vibration, bending and buckling of nanostructures as well as the results of size-dependent wave propagation analyses are discussed.

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Section: Nonlocal Strain Gradient Elasticitymentioning

confidence: 99%

“…More recently, NSGT-based continuum models have been introduced for the vibration of nanobeams [82,126,183,[186][187][188][189]. Various modified theories of elasticity are compared in Fig.…”

Section: 3d Size-dependent Vibration Of Nanobeamsmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

210

View full text Add to dashboard Cite

show abstract

“…Since the classical continuum-based approach does not have a scale parameter associated with molecular interactions, it should not be utilised for structures at small-scales [6][7][8][9]. To capture the influence of molecular interactions, the classical continuum mechanics has been modified in different ways [10][11][12], leading to a number of size-dependent theories such as the pure nonlocal elasticity (PNE) [13][14][15][16][17], couple stress models [18][19][20][21][22] and nonlocal strain gradient theory (NSGT) [23][24][25][26][27]. Employing MD calculations, it has recently been shown that the NSGT is reasonable for nanostructures [28].…”

Section: Introductionmentioning

confidence: 99%

“…Setoodeh et al [33] provided an exact solution for the nonlinear buckling of nanotubes with small-scale effects; they applied the nonlocal theory of beams to capture small-scale effects. More recently, in addition to the nonlocal theory, the NSGT has been utilised for modelling nanotubes with small-scale effects [25,[34][35][36]. For example, Li and Hu [37] applied the NSGT so as to study wave dispersion in fluid-conveying nanotubes.…”

Section: Introductionmentioning

confidence: 99%

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

Farajpour

Ghayesh

Farokhi

2019

Microfluid Nanofluid

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A coupled continuum model incorporating size influences and geometric nonlinearity is presented for the coupled motions of viscoelastic nonlinear nanotubes conveying nanofluid.A modified model of nanobeams incorporating nonlocal strain gradient effects is utilised for describing size influences on the bifurcation behaviour of the fluid-conveying nanotube. Furthermore, size influences on the nanofluid are taken into account via Beskok-Karniadakis theory. To model the geometric nonlinearity, nonlinear strain-displacement relations are employed. Utilising Hamilton's principle and the Kelvin-Voigt model, the coupled equations of nonlinear motions capturing the internal energy loss are derived. A Galerkin procedure with a high number of shape functions and a direct time-integration scheme are then employed to extract the bifurcation characteristics of the nanofluid-conveying nanotube with viscoelastic properties. A specific attention is paid to the chaotic response of the viscoelastic nanosystem. It is found that the coupled viscoelastic bifurcation behaviour is very sensitive to the flow velocity.

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“…A number of modification procedures based on the nonlocal elasticity [43][44][45][46], couple stress model [47][48][49][50][51][52], and strain gradient theory [53,54] have been proposed. More recently, a significant number of size-dependent models with microstructure-dependent deformational and nonlocal stress influences have been proposed [55,56]. The practicality and validity of nonlocal strain gradient models have been also tested and demonstrated for describing different physical phenomena at ultrasmall levels [57].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

2019

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A nonlinear vibration analysis is conducted on the mechanical behavior of axially functionally graded (AFG) microscale Timoshenko nonuniform beams. Asymmetry is due to both the nonuniform material mixture and geometric nonuniformity. Using the Timoshenko beam theory, the continuous models for translation/rotation are developed via an energy balance. Size-dependence is incorporated via the modified couple stress theory and the rotation via the Timoshenko beam theory. Galerkin’s method of discretization is applied and numerical simulations are conducted for a size-dependent vibration of the AFG microscale beam. Effects of material gradient index and axial change in the cross-sectional area on the force and frequency diagrams are investigated.

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Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory

Cited by 42 publications

References 38 publications

A review on the mechanics of nanostructures

A review on the mechanics of nanostructures

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

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