Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium

“…Moreover, the shear buckling was not investigated. For multilayered nanoplates, Pouresmaeeli et al [5] studied vibration of double-orthotropic nanoplates embedded in elastic medium. Shi et al [6] investigated vibration analysis of nanomechanical systems resonators for circular double-layer graphene sheets.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Radic et al [9] investigated buckling analysis of DONPs embedded in Pasternak elastic medium using nonlocal elasticity theory. In these works [5][6][7][8][9], the effects of non-local parameter were studied for multilayered nanoplates based on CPT and, because of using classical solutions, e.g., Navier's method as used for simply supported boundary conditions, the above-mentioned researchers were not able to investigate other boundary conditions and shear buckling. In recent years, Sarrami et al [10] studied vibration and buckling of single and multilayered graphene sheets based on non-local elasticity theory using finite strip method.…”

Section: Introductionmentioning

confidence: 99%

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Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method

Shokrani

Karimi

Tehrani

et al. 2015

J Braz. Soc. Mech. Sci. Eng.

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In this article, buckling analysis of doubleorthotropic nanoplates (DONP) embedded in elastic media under biaxial, uniaxial and shear loading is numerically studied. The analysis is based on non-local theory. Both two-variable refined plate theory (TVRPT) and first-order shear deformation plate theory (FSDT) are used to derive the governing equations. Generalized differential quadrature method (GDQM) is utilized to solve the governing equations. In buckling analysis, both in-phase and out-ofphase modes are studied. A graphene sheet is selected as the case study to investigate the numerical results. GDQM results are validated by comparing with the Navier's solutions. After validating the formulation and method of solution, the effect of non-local parameter, geometrical parameters and boundary conditions on the critical buckling load of the double-orthotropic nanoplate are investigated and discussed in detail. It is shown that the effects of non-local parameter for shear buckling are more noticeable than that of biaxial buckling. Moreover, for higher values of non-local parameter, the shear buckling is not dependent on the van der Waals and Winkler moduli.Keywords Two-variable refined plate theory Á Non-local theory Á Buckling analysis Á Generalized differential quadrature method Á Double-orthotropic nanoplate Abbreviations DONP Double-orthotropic nanoplate DQM Differential quadrature method GDQM Generalized differential quadrature method TVRPT Two-variable refined plate theory FSDT First-order shear deformation theory HSDT Higher-order shear deformation theories CPT Classical plate theory NDCBL Non-dimensional critical buckling load

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“…From elasticity points of view, the main feature of this theory is that the stress of each point does not only depend on the state of stress of that point but also on the state of stresses at its neighboring points. To date, there exist a large body of researches on nonlocal dynamics of nanoscale structures (i.e., rod-like, beam-like, plate-like, and shell-like nanostructures) including free vibration [18][19][20][21][22][23][24], forced vibrations [25][26][27], and nonlinear vibrations [28][29][30][31]. Further, vibrations of fluids-conveying SWCNTs has been widely researched by the NCT of Eringen from various aspects including free transverse vibration and dynamic instability [32][33][34][35][36] as well as longitudinal and transverse forced vibrations [37,38].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors

Kiani

2017

Acta Phys. Pol. A

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This work displays both longitudinal and transverse vibrations of magnetically affected inclined single-walled carbon nanotubes for conveying fluid flow. By employing an equivalent continuum structure on the basis of the nonlocal Timoshenko beam model as well as plug-like model for the nanofluidic flow inside the pore, the nonlocal governing equations are obtained accounting for nonlocality, frictionless nature of the inside wall, the Knudsen number, and full longitudinal and transverse interactions of the fluid flow with the single-walled carbon nanotubes. By implementing Galerkin-based assumed mode method, the equations of motion are discretized appropriately and then solved for the unknown dynamical deformation fields. The roles of nanofluidic flow velocity, small-scale parameter, inclination angle of single-walled carbon nanotube, and magnetic field strength on maximum values of longitudinal and transverse displacements are explained and discussed. The results show that the maximum dynamic deflection of the inclined nanotube would lessen by increase of the magnetic field strength. This fact is also more apparent for higher levels of fluid flow velocity. Additionally, variation of the longitudinal magnetic field has a trivial influence on the variation of longitudinal displacement. The predicted results reveal that application of the longitudinal magnetic field could be used as an efficient methodology to reduce the lateral vibrations of single-walled carbon nanotubes as nanofluidic conveyors.

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Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium

Cited by 83 publications

References 31 publications

Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory

Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory

Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method

Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors

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