Size dependent torsional vibration of nanotubes

Gheshlaghi, Behnam; Hasheminejad, Seyyed M.; Abbasion, Saeed

doi:10.1016/j.physe.2010.06.015

Cited by 46 publications

(14 citation statements)

References 15 publications

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“…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%

“…There is not a unique formula for natural frequency of torsional vibration mode using nonlocal theory. According to [41], the natural frequency for torsional vibration mode for CNTs is given by:…”

Section: Resultsmentioning

confidence: 99%

“…Suiker et al [40] compared the isotropic Cosserat continuum model with two different discrete models to examine up to which deformation level the Cosserat model accurately represents the specific underlying discrete microstructure. 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.…”

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%

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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: 98%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Fatahi-Vajari

Imam

2016

Z. Angew. Math. Phys.

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“…The simplified version of the above higher‐order model, which has been derived from the SGT, could be obtained by a selective parameter elimination. For instance, by letting

ζ_{1} = 0

and

ζ_{2} = l,

one retrieves the size‐dependent model for the torsion of a micro‐rod formulated on the basis of the modified couple stress theory reported by Gheshlaghi . Also, by allowing

ζ_{1} = ζ_{2} = 0,

one retrieves the classical equation governing the torsional vibration of a conventional rod.…”

Section: Mathematical Representationmentioning

confidence: 99%

Torsional frequency analyses of microtubules with end attachments

Mustapha

Wong

2015

Z. Angew. Math. Mech.

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This study is concerned with the mathematical modeling of microtubules for torsional vibration analysis. Microtubules (MTs) are prone to mechanical torsion, and hence conductance oscillation, when they act as molecular pathways for cargo transport. The period of this torsional oscillation has an intimate, but yet-to-be-understood relationship with the MTs' stiffness and end conditions. In the spirit of the foregoing concern, this study embarks on the characterization of the shift in the torsional resonance of an isolated MT in the presence of an end attachment in the form of either outer kinetochores (treated as a torsional spring) or a linker molecule (treated as a concentrated mass). The MT is itself idealized as a strain gradient micro-shaft, with its governing equation augmented by enriched boundary conditions due to the attachments. The solution of the model is then sought through the differential transformation method (DTM). Validation of the reduced form of the model is evaluated with benchmark results in the literature. Under a rapidly increasing magnitude of an attached rotary mass, the analyses indicate the existence of a drift of the frequency towards zero, a scenario that could induce a transition to rigid-body motion. Conversely, in the presence of spring-like elastic anchors, the analyses reveal a softening effect that increases the torsional resonant frequencies of the MT. Sensitivity assessments through Pareto analyses predict an interaction effect between the size-effect and the magnitude of an attached mass. C 2015 by the Joint Publication Board of Zygon

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