On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Malikan, Mohammad; Eremeyev, Victor A.

doi:10.3390/sym12040643

Cited by 54 publications

(23 citation statements)

References 74 publications

(103 reference statements)

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“…(23) based on the A zd A and substituting Eqs. (2) and 4into the obtained relation, the static moment stress resultants in the nonlocal state are found to be [50][51][52][53][54][55][56][57][58][59]…”

Section: Vdw Interactionmentioning

confidence: 63%

Buckling analysis of a non-concentric double-walled carbon nanotube

2020

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On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.

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Section: Vdw Interactionmentioning

confidence: 63%

Buckling analysis of a non-concentric double-walled carbon nanotube

2020

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“…In [ 26 ], the second strain gradient of Mindlin merged successfully with the nonlocal theory of Eringen. This model (NSGT) was incorporated in a lot of research performed on the nanoparticles in recent years—see e.g., [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ] and many others—and can be a proper item at the nanoscale.…”

Section: Mathematical Modelmentioning

confidence: 99%

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Malikan

Eremeyev

2020

Nanomaterials

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Among various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam.

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“…In [45] are studied the pyroelectric and pyromagnetic effects on multiphase MEE cylindrical shells subjected to a uniform axisymmetric temperature using semi-analytical finite element procedures. Eremeyev et al in [46,47] investigate the effect of flexoelectricity and flexomagnetic on nanobeams. Using FEM formulation [48,49] analyzed free vibration of orthotropic cross-ply nanoplates and nanowires.…”

Section: Introductionmentioning

confidence: 99%

Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

2021

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An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

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On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Cited by 54 publications

References 74 publications

Buckling analysis of a non-concentric double-walled carbon nanotube

Buckling analysis of a non-concentric double-walled carbon nanotube

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

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