Free vibration of nanorings/arches based on nonlocal elasticity

Wang, Chen; Duan, Wenhui

doi:10.1063/1.2951642

Cited by 94 publications

(39 citation statements)

References 48 publications

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“…1) A great deal of attention in the literature has been focused on static, dynamic, and stability analysis of micro/nano structures. These include analysis of nanobeams [12], nanorods [13], circular nanoplates [14], rectangular nanoplates [15,16], nanorings [17], and CNTs [18][19][20][21]. Majority of the studies on buckling and vibration of nanoplates are focused on single-layered (SLGS) and multilayered graphene sheets (MLGS).…”

Section: Introductionmentioning

confidence: 99%

Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method

Babaei

Shahidi

2010

Arch Appl Mech

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The elastic buckling behavior of quadrilateral single-layered graphene sheets (SLGS) under bi-axial compression is studied employing nonlocal continuum mechanics. Small-scale effects are taken into consideration. The principle of virtual work is employed to derive the governing equations. The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis. The buckling load of skew, rhombic, trapezoidal, and rectangular nanoplates considering various geometrical parameters are obtained. It is shown that nonlocal effects are very important in arbitrary quadrilateral graphene sheets and their inclusion results in smaller buckling loads. Also the effects of geometrical parameters such as aspect ratio, angle, and mode number on the buckling load decrease when scale coefficient increases, for all arbitrary quadrilateral SLGS.

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Section: Introductionmentioning

confidence: 99%

Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method

Babaei

Shahidi

2010

Arch Appl Mech

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“…Since Iijima [1] first discovered carbon nanotubes, many nanostructures have been manufactured by the experimental means, such as nanobeams [2] , nanorings [3] , and nanoplates [4] . Graphene is an important two-dimensional carbon nanostructure because nanotubes and nanorings can be viewed as deformed graphene sheets.…”

Section: Introductionmentioning

confidence: 99%

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Peng

Guo

Liu

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young's moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young's moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.

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“…Their results showed a considerable difference between the results derived from their proposed model and those of classical theories [31] . Wang et al analyzed the free vibration of nanorings/arches using the Eringen nonlocal theory with consideration of the small scale effect [32] .In another study made by Madina et al the asymmetric buckling of a shallow initially curved microbeam subjected to distributed nonlinear deflection-dependent electrostatic forced was analyzed [33] .…”

Section: Rahmani Et Al Used Nonlocal Beam Theory To Derive a Closed-mentioning

confidence: 99%

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

Hosseini

Rahmani

2018

Smart Constr Res

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Abstract:The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction. The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

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Free vibration of nanorings/arches based on nonlocal elasticity

Cited by 94 publications

References 48 publications

Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method

Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

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