Shear vibration and buckling of double-layer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects

Karimi, Morteza; Mirdamadi, Hamid Reza; Shahidi, Alireza

doi:10.1007/s00542-015-2744-8

Cited by 36 publications

(8 citation statements)

References 51 publications

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“…A variety of numerical methods such as the DQM, 63,64 GDQM, 65 and the FDM [66][67][68] are nowadays available for solving physical and engineering problems. The FDM is a powerful method for solving differential equations.…”

Section: Finite Difference Methodsmentioning

confidence: 99%

Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects

Karimi

Shahidi

2017

Proceedings of the Institution of Mechanical Engineers, Part N:

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In this article, the influence of temperature change on the vibration, buckling, and bending of orthotropic graphene sheets embedded in elastic media including surface energy and small-scale effects is investigated. To take into account the small-scale and surface energy effects, the nonlocal constitutive relations of Eringen and surface elasticity theory of Gurtin and Murdoch are used, respectively. Using Hamilton's principle, the governing equations for bulk and surface of orthotropic nanoplate are derived using two-variable refined plate theory. Finite difference method is used to solve governing equations. The obtained results are verified with Navier's method and validated results reported in the literature. The results demonstrated that for both isotropic and orthotropic material properties, by increasing the temperature changes, the degree of surface effects on the buckling and vibration of nanoplates could enhance at higher temperatures, while it would diminish at lower temperatures. In addition, the effects of surface and temperature changes on the buckling and vibration for isotropic material property are more noticeable than those of orthotropic. On the contrary, these results are totally reverse for bending problem.

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Section: Finite Difference Methodsmentioning

confidence: 99%

Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects

Karimi

Shahidi

2017

Proceedings of the Institution of Mechanical Engineers, Part N:

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“…In addition to the NET, the surface elasticity theory [87,[241][242][243] and the NSGT [244] have been also utilised for the stability of nanoscale plates, especially GSs. It has been shown that surface or strain gradient effects should be taken into consideration to capture the stiffness hardening behaviour observed in the stability of circular GSs subject to axisymmetric radial loads.…”

Section: 4c Size-dependent Buckling Of Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

212

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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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“…Moreover, in contrast to first-order shear deformation hypothesis, there is not a shear coefficient. Therefore, recently, some scholar derived the governing equations of graphene sheets via refined plate theory [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Fundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses

Jamali

Ghassemi

2018

Micro & Nano Letters

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Fundamental frequency analysis of rectangular piezoelectric nanoplates via the surface layer and non-local small-scale hypotheses is investigated in the present work. The piezoelectric nanoplate is under in-plane forces. The equilibrium governing of piezoelectric nanoplates is attained via the two variable refined plate hypothesis, and then the equations of motion are achieved utilising Hamilton's principle. To solve these equations, the finite difference method is employed. To verify the exactness of the finite difference method, the governing equations are tested by the Navier's solution. Numerical results show a good accuracy among the outcomes of the present work and some accessible cases in the literature. The numerical results show that for negative residual surface stress, as the boundary condition becomes stiffer the effect of surface layer increases, while for positive one that phenomenon is inverse.

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Shear vibration and buckling of double-layer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects

Cited by 36 publications

References 51 publications

Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects

Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects

A review on the mechanics of nanostructures

Fundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses

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