Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory

Karami, Behrouz; Shahsavari, Davood; Janghorban, Maziar

doi:10.1080/15376494.2017.1323143

Cited by 74 publications

(22 citation statements)

References 23 publications

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“…Moreover, e shows a physical constant and a=0.142 nm is the bond length of carbon-carbon atoms. By substituting equation (12) into equations (7a), (7b), the small-scale stress resultants can be obtained as [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]…”

Section: The Size-dependent Effectsmentioning

confidence: 99%

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Malikan

Eremeyev

2020

Mater. Res. Express

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This research predicts theoretically post-critical axial buckling behavior of truncated conical carbon nanotubes (CCNTs) with several boundary conditions by assuming a nonlinear Winkler matrix. The post-buckling of CCNTs has been studied based on the Euler-Bernoulli beam model, Hamilton's principle, Lagrangian strains, and nonlocal strain gradient theory. Both stiffness-hardening and stiffness-softening properties of the nanostructure are considered by exerting the second stressgradient and second strain-gradient in the stress and strain fields. Besides small-scale influences, the surface effect is also taken into consideration. The effect of the Winkler foundation is nonlinearly taken into account based on the Taylor expansion. A new admissible function is used in the Rayleigh-Ritz solution technique applicable for buckling and post-buckling of nanotubes and nanobeams. Numerical results and related discussions are compared and reported with those obtained by the literature. The significant results proved that the surface effect and the nonlinear term of the substrate affect the CCNT considerably.

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Section: The Size-dependent Effectsmentioning

confidence: 99%

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Malikan

Eremeyev

2020

Mater. Res. Express

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“…Wave propagations in nanoscale plates such as graphene sheets [287,288], smart [289] and inhomogeneous [290] nanoplates have been examined using size-dependent plate models. The majority of size-dependent studies on the wave propagation analysis have been carried out via use of the NET [291][292][293].…”

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

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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“…Thus, the introduction of Equations (15) and (16) into Equations (21) and (22), respectively, yields to the following expressions…”

Section: Theory and Formulationmentioning

confidence: 99%

“…Therefore, the research and development of these novel materials has received special attention in the last decades, especially at a nanoscale level, where classical theories are inapplicable and can fail. Hence, different methods, i.e., experimental tests, molecular dynamics (MD) simulations and non-classical mathematical formulations, have been proposed as alternative ways to predict the behavior of nanomaterials [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In work by Aifantis and Askes [36], a nonlocal strain gradient theory was proposed as an alternative non-classical method to capture both the hardening and softening stiffness mechanisms of nanostructured systems.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

Karami¹,

Janghorban²,

Dimitri³

et al. 2019

Applied Sciences

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In this work, the nonlocal strain gradient theory is applied to study the free vibration response of a Timoshenko beam made of triclinic material. The governing equations of the problem and the associated boundary conditions are obtained by means of the Hamiltonian principle, whereby the generalized differential quadrature (GDQ) method is implemented as numerical tool to solve the eigenvalue problem in a discrete form. Different combinations of boundary conditions are also considered, which include simply-supports, clamped supports and free edges. Starting with some pioneering works from the literature about isotropic nanobeams, a convergence analysis is first performed, and the accuracy of the proposed size-dependent anisotropic beam model is checked. A large parametric investigation studies the effect of the nonlocal, geometry, and strain gradient parameters, together with the boundary conditions, on the vibration response of the anisotropic nanobeams, as useful for practical engineering applications.

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Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory

Cited by 74 publications

References 23 publications

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

A review on the mechanics of nanostructures

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

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