Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories

Daneshmehr, Alireza; Rajabpoor, Amir; Hadi, Amin

doi:10.1016/j.ijengsci.2015.05.011

Cited by 158 publications

(29 citation statements)

References 40 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

210

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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

210

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“…Hosseini-Hashemi et al [175] derived Levy solutions for critical buckling loads and natural frequencies of isotropic nanoplates. Daneshmehr et al [176][177] extended the application of the nonlocal TSDT to the buckling [176] and free vibration analysis [177] of FG nanoplates.…”

Section: Nonlocal Models Based On the Tsdtmentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

324

112

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This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

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“…Recently, several non-classical theories such as couple stress theory (Mindlin and Tiersten, 1962), modified couple stress theory (Yang et al, 2002), strain gradient theory (Mindlin, 1964), nonlocal elasticity theory (Eringen, 1972), and nonlocal strain gradient theory (Lim et al, 2015) try to capture the size effect in the structures. The scientific literature includes many papers based on different non-classical theories on the mechanical analysis of micro-and nano-sized structures such as micro/nanorod (Bahrami, 2017b), micro/nanobeam ( While there are many papers in the literature regarding the effects of thickness and small scale on the frequency ratio of nanobeams and nanoplates using Eringen's nonlocal theory, unfortunately, most papers presented the thickness effect on the frequency ratio for fully simply supported cases due to simplicity of the calculation in this case (Aghababaei and Reddy, 2009;Aydogdu, 2009;Bahrami and Teimourian, 2016;Daneshmehr et al, 2015;Eltaher et al, 2012;Natarajan et al, 2012;Rahmani and Pedram, 2014;Reddy, 2007;Thai, 2012). As a result, the true effect of the thickness to length ratio on the frequency ratio of nanobeams and nanoplates was not captured and reported at all.…”

Section: Introductionmentioning

confidence: 99%

Effect of the thickness to length ratio on the frequency ratio of nanobeams and nanoplates

Bahrami¹,

Shiri²,

Khosravi³

2019

Journal of Theoretical and Applied Mechanics

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This communication presents the effect of thickness on the frequency ratio of nanobeams and nanoplates using Eringen's nonlocal theory. Although there exist numerous works regarding the effects of thickness and small scale on the frequency ratio of nanobeams and nanoplates, none has captured and reported the true effects. The main intention of this communication is to correct the misunderstanding regarding this issue. It was found that the frequency ratio is indeed dependent on the thickness to length ratio and its variation with respect to thickness to length ratio is highly dependent on the mode number, combination of boundary conditions, plate aspect ratio, and the nonlocal parameter.

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Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories

Cited by 158 publications

References 40 publications

A review on the mechanics of nanostructures

A review on the mechanics of nanostructures

A review of continuum mechanics models for size-dependent analysis of beams and plates

Effect of the thickness to length ratio on the frequency ratio of nanobeams and nanoplates

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