Analysis of Free Torsional Vibration in Carbon Nanotubes Embedded in a Viscoelastic Medium

Arda, Mustafa; Aydoğdu, Metin

doi:10.12913/22998624/2361

Cited by 12 publications

(12 citation statements)

References 19 publications

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“…In this section, comparison between the results obtained in this work and the results available in MD [56] and nonlocal theory [42] are discussed. But first, the formula for the natural frequency of torsional vibration mode using nonlocal theory is provided below.…”

Section: Resultsmentioning

confidence: 87%

“…In this method, there is not a close form formula for the results that are obtained. It is clear that unlike DM, some of nonlocal theory formulae like [39,41] predict the increase in natural frequency with increase in the scale parameter, while the others like [42] predict the opposite. The atomistic methods that have relatively more accurate results predict a decrease in the natural frequency with increase in the scale parameter effect [56].…”

Section: Resultsmentioning

confidence: 98%

“…The first column shows the n and m chiral indices, the second and third columns show the SWCNT radius and length and the next four columns are the results from MD [56], DM, CCM and nonlocal [42] theories. Throughout this paper, the SWCNT is assumed to be isotropic with the material properties taken to be: shear modulus G = 0.392 − 0.412 TPa, mass density ρ * = 2491 kg m 3 and Poisson's ratio ν = 0.193 − 0.217 [56].…”

Section: Resultsmentioning

confidence: 99%

“…Gheshlaghi et al [41] studied torsional vibration of nanotubes using a modified couple stress theory. Arda and Aydogdu [42] investigated damping and elastic effect of medium to the torsional vibration of CNTs. Selim [43] studied torsional vibration of SWCNTs subjected to initial compressive stresses.…”

Section: Introductionmentioning

confidence: 99%

“…Also, atomistic methods [55][56][57] are costly and difficult to implement particularly for large-scale systems. On the other hand, CCM models such as elastic beam models [58] used to study the torsional vibration of CNTs do not consider scale effects, while in the nonlocal theory [41][42][43][44][45], as mentioned above, the scale parameter does not enter the theory directly.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Fatahi-Vajari

Imam

2016

Z. Angew. Math. Phys.

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This paper investigates the torsional vibration of single-walled carbon nanotubes (SWCNTs) using a new approach based on doublet mechanics (DM) incorporating explicitly scale parameter and chiral effects. A fourth-order partial differential equation that governs the torsional vibration of nanotubes is derived. Using DM, an explicit equation for the natural frequency in terms of geometrical and mechanical property of CNTs is obtained for both the Zigzag and Armchair nanotube for the torsional vibration mode. It is shown that chiral effects along with the scale parameter play a significant role in the vibration behavior of SWCNTs in torsional vibration mode. Such effects decrease the natural frequency obtained by DM compared to the classical continuum mechanics and nonlocal theory predictions. However, with increase in the length and/or the radius of the tube, the effect of the chiral and scale parameter on the natural frequency decreases.Mathematics Subject Classification. 70G60 · 70J30 · 35B99 · 00A72.

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Section: Resultsmentioning

confidence: 87%

Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Fatahi-Vajari

Imam

2016

Z. Angew. Math. Phys.

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Torsional vibrational analysis of irregular single-walled carbon nanotube with elastic-support boundary conditions

Selim¹,

Alotaibi²,

Soltani³

et al. 2023

Journal of Materials Research and Technology

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Nonlinear coupled axial–torsional vibration of single‐walled carbon nanotubes using homotopy perturbation method

Fatahi-Vajari¹,

Azimzadeh²,

Hussain³

2019

Micro & Nano Letters

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This work analyses the nonlinear coupled axial-torsional vibration of single-walled carbon nanotubes (SWCNTs) based on numerical methods. Two-second order partial differential equations that govern the nonlinear coupled axial-torsional vibration for such nanotube are derived. First, these equations are reduced to ordinary differential equations using the Galerkin method and then solved using homotopy perturbation method (HPM) to obtain the nonlinear natural frequencies in coupled axial-torsional vibration mode. It is found that the obtained frequencies are complicated due to coupling between two vibration modes. The dependence of boundary conditions, vibration modes and nanotubes geometry on the nonlinear coupled axial-torsional vibration characteristics of SWCNTs are studied in detail. It was shown that boundary conditions and maximum initial vibration velocity have significant effects on the nonlinear coupled axial-torsional vibration response of SWCNTs. It was also seen that unlike the linear model if the maximum vibration velocity increases, the natural frequencies of vibration increases too. To show the effectiveness and ability of this method, the results obtained with HPM are compared with the fourth-order Runge-Kutta numerical results and good agreement is observed. To the knowledge of authors, the results given herein are new and can be used as a foundation work for future work.

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Analysis of Free Torsional Vibration in Carbon Nanotubes Embedded in a Viscoelastic Medium

Cited by 12 publications

References 19 publications

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Torsional vibrational analysis of irregular single-walled carbon nanotube with elastic-support boundary conditions

Nonlinear coupled axial–torsional vibration of single‐walled carbon nanotubes using homotopy perturbation method

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