Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings

Karimi, Morteza; Shahidi, Alireza

doi:10.1007/s00339-017-0828-2

Cited by 33 publications

(12 citation statements)

References 45 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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“…A variety of numerical methods can be used for solving problems in physical and engineering sciences; these are such as: generalized differential quadrature method [31,32] and finite difference method [33][34][35][36]. The finite difference method is a powerful method employed for solving differential equations.…”

Section: Finite Difference Methodsmentioning

confidence: 99%

The effects of surface stress and nonlocal small scale on the uniaxial and biaxial buckling of the rectangular piezoelectric nanoplate based on the two variable-refined plate theory

Fathi

Ghassemi

2017

J Braz. Soc. Mech. Sci. Eng.

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The effects of surface stress and nonlocal small scale on the uniaxial and biaxial buckling of the rectangular and skew piezoelectric nanoplate were investigated based on the two variable-refined plate theory (TVRPT). The governing equations were derived using the principle of virtual work and then it was solved using the finite difference method. Finite difference solutions were validated by Navier's method and journal references. A parametric study was conducted to investigate the influences of the external electric voltage, nonlocal parameter, different boundary condition, nanoplate thickness, and aspect ratio on the surface effect of uniaxial and biaxial buckling. Numerical results obtained showed that the influence of surface stress on the buckling of the rectangular piezoelectric nanoplate was enhanced by augmenting the nonlocal parameter, external electric voltage, and aspect ratio while it was decreased in the thicker nanoplate. The present work could be very useful in designing micro and nanodevices using smart nanocomposites.

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“…∇ 2 is the Laplace operator and also e 0 a is the non-local parameter. Using the Hamilton's principle, the governing equations of motion for the piezoelectric nanoplate are derived as follows [19,20]:…”

Section: Formulationmentioning

confidence: 99%

“…Therefore, the bending and shearing electric field is stated as follows: Based on reference [19,20], the stress resultants are written in terms of the displacement components as follows:…”

Section: Formulationmentioning

confidence: 99%

“…The SS boundary conditions are indicated as follows: fundamental frequency with surface effect fundamental frequency without surface effect (19) The in-plane load and non-local parameter are equal to zero. From Table 2, it can be seen that in all cases, the current results are in suitable match with those reported by Yan and Jiang [4].…”

Section: Ss Boundary Conditionmentioning

confidence: 99%

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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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Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings

Cited by 33 publications

References 45 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

The effects of surface stress and nonlocal small scale on the uniaxial and biaxial buckling of the rectangular piezoelectric nanoplate based on the two variable-refined plate theory

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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