On the dynamics of nano-frames

Russillo, Andrea Francesco; Failla, Giuseppe; Alotta, Gioacchino; Sciarra, Francesco Marotti de; Barretta, Raffaele

doi:10.1016/j.ijengsci.2020.103433

Cited by 38 publications

(13 citation statements)

References 91 publications

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“…Studies expressing a paradox in nonlocal elasticity were presented [22,23]. Various scientific articles related to investigations of various small-scaled elements/structures such as porous FG nanobeam [24], FG nanobeam/microbeam [25][26][27][28][29][30][31][32][33], microplate [34], nanoplate [35], nanobeam/microbeam [36][37][38], porous microplate [39], nanowire [40,41], nanotube [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] and other small-scaled elements/structures [61][62][63][64][65][66][67][68] can be found in open literature. Also, in addition to the above-mentioned studies, scholars presented the papers…”

Section: F I G U R E 1 Demonstration Of Bn Sheetmentioning

confidence: 99%

Finite element formulation for nano‐scaled beam elements

2021

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In the present study, size-dependent buckling and free vibration behaviors of single-walled boron nitride nanotube (SWBNNT) are performed in conjunction with various size-dependent elasticity theories. Modified couple stress theory (MCST) and Eringen's nonlocal elasticity theory are used for size-dependent models of SWBNNT. Also, the buckling loads and frequencies are obtained by using local theory to emphasize the effects and differences of these sizedependent theories. Consequently, three different elasticity theories (two nonclassical and one classical) are utilized to achieve the detailed buckling and vibration analyses of SWBNNT. In this study, the buckling loads and frequencies of SWBNNTs are obtained via presented finite element formulation. In the finite element procedures based on two different size-dependent elasticity theories, matrices containing the small size parameter are derived. With these matrices containing the small size parameters, eigenvalue problems for buckling and free vibration analyses are formed. The buckling loads and frequency values of the SWBNNTs under the size effect are obtained. The influences of the dimensionless nonlocal parameter, dimensionless material length scale parameter, lengthto-diameter ratio and boundary conditions on nanotube's buckling and vibration characteristics are investigated. In addition to these influences, the rotary inertia effect neglected in many other studies is also examined.

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Section: F I G U R E 1 Demonstration Of Bn Sheetmentioning

confidence: 99%

Finite element formulation for nano‐scaled beam elements

2021

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“…Consequently, only systems with limited amounts of atoms and molecules can be practically investigated, thus an alternative modeling approach with a superior computational efficiency is deemed essential. Collaboration between a structural-mechanics model (bar, beam, plate, and shell) and non-classical elasticity theory has been carried out by researchers to develop an alternative tool to characterize mechanical responses of small-sized structures [ 12 , 13 , 14 , 15 , 16 , 17 , 18 ]. This integrated modeling approach could account for the small-scale effect as well as the size-dependent effect with good balance between accuracy and computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Strain-Gradient Bar-Elastic Substrate Model with Surface-Energy Effect: Virtual-Force Approach

et al. 2022

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This paper presents an alternative approach to formulating a rational bar-elastic substrate model with inclusion of small-scale and surface-energy effects. The thermodynamics-based strain gradient model is utilized to account for the small-scale effect (nonlocality) of the bar-bulk material while the Gurtin–Murdoch surface theory is adopted to capture the surface-energy effect. To consider the bar-surrounding substrate interactive mechanism, the Winkler foundation model is called for. The governing differential compatibility equation as well as the consistent end-boundary compatibility conditions are revealed using the virtual force principle and form the core of the model formulation. Within the framework of the virtual force principle, the axial force field serves as the fundamental solution to the governing differential compatibility equation. The problem of a nanowire embedded in an elastic substrate medium is employed as a numerical example to show the accuracy of the proposed bar-elastic substrate model and advantage over its counterpart displacement model. The influences of material nonlocality on both global and local responses are thoroughly discussed in this example.

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“…Mechanical structure models such as rod [1][2][3][4][5][6][7][8][9][10][11] and beam [12][13][14][15][16][17][18][19][20][21][22][23][24][25] form the basis of studies in the nonlocal mechanics of nanostructures. Also, recently, studies that mention mechanical analyses with nonlocal elasticity of discrete structures such as truss and frame [26][27][28] have entered the scientific literature.…”

Section: Introductionmentioning

confidence: 99%

Examination of How Size-Effect Modifies the Stiffness and Mass Matrices of Nanotrusses/Nanoframes

Numanoğlu

2021

International Journal of Engineering and Applied Sciences

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The effect of the nonlocal parameter on the free vibration analysis of nano scaled trusses and frames is examined. Accordingly, firstly, the axial and bending vibrations of the nano scaled longitudinal element are formulated. Simple rod and Euler-Bernoulli assumptions are considered for axial and bending vibrations, respectively. Finite element matrices are obtained by applying the average weighted residue to the nonlocal equation of motion for free vibration. These matrices are combined according to the freedoms of longitudinal element and the matrix displacement method is explained for structures consisting of discrete longitudinal elements. It is discussed how the classical stiffness and mass matrices are modified by the atomic parameter.

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On the dynamics of nano-frames

Cited by 38 publications

References 91 publications

Finite element formulation for nano‐scaled beam elements

Finite element formulation for nano‐scaled beam elements

Strain-Gradient Bar-Elastic Substrate Model with Surface-Energy Effect: Virtual-Force Approach

Examination of How Size-Effect Modifies the Stiffness and Mass Matrices of Nanotrusses/Nanoframes

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