Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes

Mehralian, Fahimeh; Beni, Yaghoub Tadi; Zeverdejani, Mehran Karimi

doi:10.1016/j.physb.2017.03.030

Cited by 108 publications

(26 citation statements)

References 81 publications

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“…As can be seen, our results are completely matched with those from the literature. Table 3 shows the results of a carbon nanotube (CNT) that was studied according to NSGT by [69] in a shell-like structure and by [70] in a beam-like structure. As can be observed, our results match well with those of both pieces of literature.…”

Section: Results Validationmentioning

confidence: 99%

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Malikan

Eremeyev

2020

Symmetry

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The fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the nanobeams include an internal damping feature. To this end, a closed-circuit condition is considered taking converse piezo–flexoelectric behavior. The kinematic displacement of the classical beam using Lagrangian strains, also applying Hamilton’s principle, creates the needed frequency equation. The natural frequencies are measured in nanoscale by the available nonlocal strain gradient elasticity model. The linear Kelvin–Voigt viscoelastic model here defines the inner viscoelastic coupling. An analytical solution technique determines the values of the numerical frequencies. The best findings show that the viscoelastic coupling can directly affect the flexoelectricity property of the material.

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Section: Results Validationmentioning

confidence: 99%

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Malikan

Eremeyev

2020

Symmetry

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“…and a are a scale parameter for calibrating the theoretical model and the internal characteristics length of the nanotube, respectively [54,55]. The strain gradient parameter and the nonlocal parameter are determined using experimental measurements or MD simulations [21,56,57]. For instance, Li et al [35] obtained the scale parameters of carbon 6 nanotubes for the wave propagation analysis via MD simulations.…”

Section: Size-dependent Formulation and Solution Techniquementioning

confidence: 99%

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

Farajpour

Ghayesh

Farokhi

2019

International Journal of Mechanical Sciences

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In this paper, a scale-dependent coupled nonlinear continuum-based model is developed for the mechanical behaviour of imperfect nanoscale tubes incorporating both the effect of the stress nonlocality and strain gradient effects. The scale effects on the nonlinear mechanics are taken into consideration employing a modified elasticity theory on the basis of a refined combination of Eringen's elasticity and the strain gradient theory. According to the Euler-Bernoulli theory of beams, the nonlocal strain gradient theory (NSGT) and Hamilton's principle, the potential energy, kinetic energy and the work performed by harmonic loads are formulated, and then the coupled scale-dependent equations of the imperfect nanotube are derived. Finally, Galerkin's scheme, as a discretisation technique, and the continuation method, as a solution procedure for ordinary differential equations, are used. The effects of geometrical imperfections in conjunction with other nanosystem parameters such as the nonlocal coefficient as well as the strain gradient coefficient on the coupled large-amplitude mechanical behaviour are explored and discussed.

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“…In general, the nonlocal and strain gradient parameters are obtained from experimental data or the results of molecular dynamics (MD). In the literature, MD simulations were performed to determine these scale parameters for both nanotubes and fluid-conveying nanotubes (Mohammadi et al, 2018;Mehralian et al, 2017a;Mehralian et al, 2017b). The values of nonlocal and strain gradient parameters, which are taken in the present paper, are in the recommended range obtained by MD simulations.…”

Section: A Nsgt-based Modellingmentioning

confidence: 99%

A nonlinear viscoelastic model for NSGT nanotubes conveying fluid incorporating slip boundary conditions

Farajpour

Farokhi²,

Ghayesh

2019

Journal of Vibration and Control

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A nonlinear viscoelastic model is developed for the dynamics of nanotubes conveying fluid. The influences of strain gradients and stress nonlocality are incorporated via a nonlocal strain gradient theory (NSGT). Since at nanoscales, the assumptions of no-slip boundary conditions are not valid, the Beskok-Karniadakis theory is used to overcome this problem. The coupled nonlinear differential equations are derived via performing an energy/work balance. The derived equations along the transverse and axial axes are simultaneously solved to obtain the nonlinear frequency response. For this purpose, Galerkin's technique together with a continuation method are utilised. The frequency response is investigated in both subcritical and supercritical flow regimes.

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Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes

Cited by 108 publications

References 81 publications

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

A nonlinear viscoelastic model for NSGT nanotubes conveying fluid incorporating slip boundary conditions

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