On dynamic analysis of nanorods

Numanoğlu, Hayri Metin; Akgöz, Bekir; Cívalek, Ömer

doi:10.1016/j.ijengsci.2018.05.001

Cited by 189 publications

(60 citation statements)

References 96 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Among 4 them, Eringen's constitutive model is one of the most widely used 5 non-local theories, as it incorporates a small-scale parameter into 6 the constitutive equation to capture micro/nano structural effects 7 in continuous media [1][2][3][4] . It is originally formulated in an inte- 8 gral form, and simplified to a differential counterpart; yet, due to 9 paradoxical outcomes of the latter for certain mechanical problems 10 [5][6][7] , the former form has also been substantially used [8][9][10][11][12][13] . 11 This study concentrates on integral form of Eringen's two-phase 12 local/nonlocal model [14] to investigate the behaviour of specific 13 discrete systems.…”

Section: Introductionmentioning

confidence: 99%

“…It is originally formulated in an inte- 8 gral form, and simplified to a differential counterpart; yet, due to 9 paradoxical outcomes of the latter for certain mechanical problems 10 [5][6][7] , the former form has also been substantially used [8][9][10][11][12][13] . 11 This study concentrates on integral form of Eringen's two-phase 12 local/nonlocal model [14] to investigate the behaviour of specific 13 discrete systems. In fact, linking discrete systems to continuum ap- 14 proaches dates back to early molecular models of 19th century, 15 through which the first attempts to derive the constitutive equa- 16 tions of continua was initiated [15,16] .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Deformation of atomic models and their equivalent continuum counterparts using Eringen’s two-phase local/nonlocal model

Tuna

Kırca

Trovalusci

2019

Mechanics Research Communications

View full text Add to dashboard Cite

Available online xxx Keywords: Two-phase local/nonlocal model Eringen Atomic array Finite element method a b s t r a c t The aim of this contribution is to formulate equivalent continuum finite element model for twodimensional atomic arrays under plane-stress condition, based on Eringen's two phase local/nonlocal model. The interaction between the atoms is modelled using translational and rotational linear elastic springs including both nearest and second nearest neighbor relations. Explicit relations between those set of springs and material properties of associated continuum model is looked for by means of equivalency of potential energy stored in atomic bonds and strain energy of continuum. Possibility of reducing computational burden of full atomic models by equivalent continuum models is discussed. This study may be regarded as the first step in composing a partitioned-domain multiscale model; with possibly smoother transition between coarse and fine scales due to the ability of nonlocal continuum model in incorporating long-range interactions. .tr (M. Tuna). D atomic chain and 2-D atomic array models are considered. In-20 teratomic potentials are modelled using linear elastic translational 21 and rotational springs, for both the nearest, and second nearest 22 43 https://doi.Please cite this article as: M. Tuna, M. Kirca and P. Trovalusci, Deformation of atomic models and their equivalent continuum counterparts using Eringen's two-phase local/nonlocal model, Mechanics Research Communications, https://doi.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deformation of atomic models and their equivalent continuum counterparts using Eringen’s two-phase local/nonlocal model

Tuna

Kırca

Trovalusci

2019

Mechanics Research Communications

View full text Add to dashboard Cite

show abstract

“…It is found that for small lengths, scale effects are noticeable while the nonlocal and local frequencies are approximately the same after a certain length (L>20 nm). More recently, the nonlocal rod model has been employed to analyse the longitudinal free vibration of nanorods for different boundary conditions including an attached mass and an attached spring [95]; it was found that the mass attachment reduces the axial frequency of nanorods.…”

Section: 1a Nonlocal Rod Modelmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

212

View full text Add to dashboard Cite

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.

show abstract

“…A large number of studies related to vibration characteristics of intact and cracked FG uniform beams are available [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Furthermore the studies have been extended in mechanical analysis of small-sized structures [23][24][25][26][27][28][29][30][31]. Studies on non-uniform FG beams can also be found in literature [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], while studies on non-uniform FG beams with an imperfection are scarce.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of cracked functionally graded non-uniform beams

Shabani

Cunedioĝlu

2020

Mater. Res. Express

View full text Add to dashboard Cite

This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

show abstract

On dynamic analysis of nanorods

Cited by 189 publications

References 96 publications

Deformation of atomic models and their equivalent continuum counterparts using Eringen’s two-phase local/nonlocal model

Deformation of atomic models and their equivalent continuum counterparts using Eringen’s two-phase local/nonlocal model

A review on the mechanics of nanostructures

Free vibration analysis of cracked functionally graded non-uniform beams

Contact Info

Product

Resources

About