Combining surface effects and non‐local two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates

Karimi, Morteza; Haddad, Hojjat Allah; Shahidi, Alireza

doi:10.1049/mnl.2014.0651

Cited by 35 publications

(18 citation statements)

References 30 publications

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“…Various nonlocal plate models such as the Kirchhoff plate theory [250][251][252][253][254], first-order shear deformation model [55,255], two-variable refined theory of plates [256,257] and higher-order shear deformation model [258][259][260] have been employed so as to examine the linear vibration of nanoscale plates. On the other hand, to solve the size-dependent differential equations of these nonlocal plate models, different solution methods such as analytical approaches [261][262][263],…”

Section: 4d Size-dependent Vibration Of Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

201

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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: 4d Size-dependent Vibration Of Nanoplatesmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

201

View full text Add to dashboard Cite

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“…The buckling problems of simply supported nanoplates were analyzed by Wang and Wang [23] considering both non-local elasticity and surface effects. Karimi et al [24] investigated vibration, shear and biaxial buckling of rectangular nanoplates, by using the non-local two variable refined plate theory. Daneshmehr et al [25] studied the free vibration problems of functionally graded nanoplates via non-local elasticity and high order theories.…”

Section: Introductionmentioning

confidence: 99%

“…∂x∂y dxdy (24) where N, M and Q are the resultant forces, moments and shear forces, respectively. They are defined by:…”

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confidence: 99%

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Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Wang

Zhang

2018

Coatings

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In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

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“…The results showed that the piezoelectric effect had a tendency to increase the stiffness of the plate, and vice versa for the magnetostrictive effect. Karimi et al (2015a) investigated surface effects and non-local two variable refined plate theories that were combined on the shear/biaxial buckling and vibration of rectangular nanoplates. Their results showed that by increasing the non-local parameter, the effects of surface on the buckling and vibration increased.…”

Section: Introductionmentioning

confidence: 99%

Bending, buckling, and forced vibration analyses of nonlocal nanocomposite microplate using TSDT considering MEE properties dependent to various volume fractions of CoFe2O4-BaTiO3

Mohammadimehr

Rostami

2017

jtam

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In this article, the bending, buckling, free and forced vibration behavior of a nonlocal nanocomposite microplate using the third order shear deformation theory (TSDT) is presented. The magneto-electro-elastic (MEE) properties are dependent on various volume fractions of CoFe 2 O 4 -BaTiO 3 . According to Maxwell's equations and Hamilton's principle, the governing differential equations are derived. These equations are discretized by using Navier's method for an MEE nanocomposite Reddy plate. The numerical results show the influences of elastic foundation parameters such as aspect ratio, length to thickness ratio, electric and magnetic fields and various volume fractions of CoFe 2 O 4 -BaTiO 3 on deflection, critical buckling load and natural frequency. The natural frequency and critical buckling load increases with the increasing volume fraction of CoFe 2 O 4 -BaTiO 3 , also the amplitude vibration decreases with an increase in the volume fraction. This model can be used for various nanocomposite structures. Also, a series of new experiments are recommended for future work.Keywords: bending and buckling analysis, free and forced vibration analysis, nonlocal nanocomposite microplate, various volume fractions of CoFe 2 O 4 -BaTiO 3

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Combining surface effects and non‐local two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates

Cited by 35 publications

References 30 publications

A review on the mechanics of nanostructures

A review on the mechanics of nanostructures

Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Bending, buckling, and forced vibration analyses of nonlocal nanocomposite microplate using TSDT considering MEE properties dependent to various volume fractions of CoFe2O4-BaTiO3

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