Vibration and buckling analysis of nanotubes (nanofibers) embedded in an elastic medium using Doublet Mechanics

Buckling analysis of functionally graded (FG) nanobeams is examined using doublet mechanics theory. The material properties of FG nanobeams change with the thickness coordinate. A periodic nanostructure model is considered in FG nanobeams which has a simple crystal square lattice type and Euler-Bernoulli beam theory is used in the formulation. Softening or hardening material behaviour has been observed by changing chiral angle of the considered FG periodic nanobeams in the present doublet mechanics theory. Unlike other size dependent theories such as nonlocal stress gradient elasticity theory, couple stress theory, strain gradient theory, this mechanical response (softening or hardening) is seen for the first time in doublet mechanics theory. Mechanical material responses are directly affected by the atomic structure of the considered material in the doublet mechanics theory. Firstly, micro-stress and micro-strain relations are obtained for the considered nanostructure model in doublet mechanics theory. Then, these microequations are transformed to macroequations in the present doublet mechanics theory. Thus, more physical and accurate mechanical results can be obtained in nanostructures using the doublet mechanics theory. After developing the mathematical formulations of FG periodic nanobeams, Ritz method is applied to obtain the critical buckling loads for different boundary conditions. Comparison of example studies with the present doublet mechanics model is presented for verification, and effects of chiral angle on stability response of periodic FG nanobeams are discussed.

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“…Fig. 1 Functionally graded nanobeam the DM theory, the strain energy of the nanobeam ( U s ) can be determined as [39]:…”

Section: Theory and Mathematical Formulationmentioning

confidence: 99%

“…Analytical solutions of nonlinear stability and vibration of imperfect and curved carbon nanotubes have been obtained by using DM theory in [33,34]. Beside these studies, DM model has been applied to investigate the static and dynamic analyses of nanostructures [35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory

Gül

Aydoğdu

2021

J Braz. Soc. Mech. Sci. Eng.

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“…Authors continued their study to investigate the vibration and buckling response of embedded nanotubes using the size-dependent DM. Nanotube was modeled based on the Euler-Bernoulli beam embedded in an elastic medium and reported solution for Free vibration frequencies and critical buckling loads under simply supported and clamped boundary conditions [222]. Furthermore, authors modeled embedded DWCNTs based on the Euler-Bernoulli beams within the framework of DM and reported numerical results for free vibration and buckling of considered DWCNTs system, for simply supported boundary conditions.…”

Section: Nonlocal Doublet Mechanicsmentioning

confidence: 99%

Advances in modelling and analysis of nano structures: a review

Chandel

Wang

Talha

2020

Nanotechnology Reviews

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AbstractNanostructures are widely used in nano and micro-sized systems and devices such as biosensors, nano actuators, nano-probes, and nano-electro-mechanical systems. The complete understanding of the mechanical behavior of nanostructures is crucial for the design of nanodevices and systems. Therefore, the flexural, stability and vibration analysis of various nanostructures such as nanowires, nanotubes, nanobeams, nanoplates, graphene sheets and nanoshells has received a great attention in recent years. The focus has been made, to present the structural analysis of nanostructures under thermo-magneto-electro-mechanical loadings under various boundary and environmental conditions. This paper also provides an overview of analytical modeling methods, fabrication procedures, key challenges and future scopes of development in the direction of analysis of such structures, which will be helpful for appropriate design and analysis of nanodevices for the application in the various fields of nanotechnology.

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“…Kojic et al [37] reformulated DM using the FEM to further expand the capabilities of the FEM. Also, notable are articles on wave propagation in granular media [38,39] and medical applications [40,41] as well as recent articles on vibration analysis of single walled carbon nanotubes, [42][43][44][45][46] single layered graphene sheets, [47] nanorods embedded in an elastic medium, [48] and modeling of nanorods. [49] F I G U R E 1 A doublet particle [42] F I G U R E 2 Translations and rotations of doublet nodes [16] However, bending analysis of Euler-Bernoulli and Timoshenko nanobeams based on DM does not seem to have been considered so far, which is the subject of study of the present paper.…”

Section: Introductionmentioning

confidence: 99%

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

2018

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By taking the effect of the scale parameter explicitly into account, bending behavior of Euler‐Bernoulli and Timoshenko nanobeams is studied using doublet mechanics. In addition, the effect of chirality on the softening or hardening behavior of an Euler‐Bernoulli nanobeam in bending is studied by taking the effect of the chiral angle explicitly into account. For the bending of the Timoshenko nanobeam the effect of the scale parameter and chirality on the axial and shear stresses is studied and the results are compared with the gradient and Eringen‐like models. It is shown that as the chiral angle increases, a simply supported Timoshenko nanobeam under a uniform loading changes from a softening to a hardening nanobeam indicating that chirality has a pronounced effect on the bending response of the nanobeams.

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Vibration and buckling analysis of nanotubes (nanofibers) embedded in an elastic medium using Doublet Mechanics

Cited by 20 publications

References 25 publications

Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory

Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory

Advances in modelling and analysis of nano structures: a review

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

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