A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

doi:10.1016/j.ijengsci.2016.07.008

Cited by 281 publications

(63 citation statements)

References 41 publications

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“…The majority of size-dependent studies on the wave propagation analysis have been carried out via use of the NET [291][292][293]. The surface elasticity theory [294,295] and the NSGT [296,297] have been also utilised to explore the size-dependent wave propagation in nanoplates. It was found that increasing nonlocal parameter strengthens the dispersion degree.…”

Section: 4e Size-dependent Wave Propagations In Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

192

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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: 4e Size-dependent Wave Propagations In Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

192

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“…ceramics and metal) and the material properties of FG cylindrical shell varies continuously and consistently from the material properties of ceramics on the inner surface of the cylindrical shell to the properties of the metal on the outer surface as a function of constituent's volume fraction. Variation in volume fraction of metal ∫ ∫ (4) To extract the governing equations of FG nanotubes, Hamilton's principle is utilized as below:…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…The bending, buckling and vibration behaviors of axially FG nanobeams were investigated by Li et al and the critical buckling force and natural frequency were shown size dependent [3]. Ebrahimi et al examined the wave propagation of FG nanoplate under nonlinear thermal loading and the influence of different parameters such as gradient index, temperature distribution and length scale parameter on the wave dispersion was presented [4]. The buckling of cylindrical and conical panels and shells of laminated composite, FGM and carbon nanotube reinforced functionally graded cases were examined by Civalek and the effects of material and geometrical parameters on buckling response were shown [5].…”

Section: Introductionmentioning

confidence: 99%

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Beni¹,

Mehralian²

2017

International Journal of Engineering &Amp; Applied Sciences

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In the current study, the size dependent free vibration of shear deformable functionally graded (FG) nanotubes is investigated. The nanotube is modeled as cylindrical shell which contains small scale effects by using the nonlocal strain gradient theory. Material properties of the FG nanotube are assumed to be variable along thickness direction according to power law distribution. The Hamilton's principle is implemented to derive the governing equations and boundary conditions. The numerical results are presented for simply supported FG nanotube and the influence of different parameters, such as nonlocal parameter, length scale parameter, length, thickness and power law index on frequency of FG nanotube are extensively studied. The results reveal that the frequency is significantly size dependent.

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“…However, in several problems involving inherent material heterogeneity with length scale similar to the geometry of the considered problem, the use of mesoscale approaches in linear context, yields satisfactory prediction of experimental data [4]. In this context, the nonlocal mechanics, defined in terms of gradients [5][6][7] or integrals [8,9] of the state variables of the problem, provides interesting forecast of wave dispersion and shear bands as well as strain localization in mechanical interfaces [10,11]. Non-local approaches result into mesoscale applications of continuum mechanics theory involving non-homogeneous media introducing the non-local terms to account for the heterogeneity of the representative volume elements of the considered problem.…”

Section: Introductionmentioning

confidence: 99%

A Fractional Approach to Non-Newtonian Blood Rheology in Capillary Vessels

Alotta

Failla

et al. 2019

J Peridyn Nonlocal Model

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In small arterial vessels, fluid mechanics involving linear viscous fluid does not reproduce experimental results that correspond to non-parabolic profiles of velocity across the vessel diameter. In this paper, an alternative approach is pursued introducing long-range interactions that describe the interactions of non-adjacent fluid volume elements due to the presence of red blood cells and other dispersed cells in plasma. These non-local forces are defined as linearly dependent on the product of the volumes of the considered elements and on their relative velocity. Moreover, as the distance between two volume elements increases, the non-local forces decay with a material distance-decaying function. Assuming that decaying function belongs to a power-law functional class of real order, a fractional operator of the relative velocity appears in the resulting governing equation. It is shown that the mesoscale approach involving Hagen-Poiseuille law is able to reproduce experimentally measured profiles of velocity with a great accuracy. Additionally as the dimension of the vessel increases, non-local forces become negligible and the proposed model reverts to the classical Hagen-Poiseuille model.

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A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates

Cited by 281 publications

References 41 publications

A review on the mechanics of nanostructures

A review on the mechanics of nanostructures

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

A Fractional Approach to Non-Newtonian Blood Rheology in Capillary Vessels

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