Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality

Fazelzadeh, S. Ahmad; Ghavanloo, Esmaeal

doi:10.1016/j.compstruct.2011.10.014

Cited by 72 publications

(58 citation statements)

References 39 publications

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“…do not take into account the size effects . The justification of this simplification is confirmed by both the latest studies and some subsequent limitations concerning the nanotube sizes. So, S.A. Fazelzadeh et al.…”

Section: On Applicability Of the Shell Theory For Short Carbon Nanotubesmentioning

confidence: 93%

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Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

Mikhasev

Ботогова

2016

Z Angew Math Mech

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Buckling of short multi-walled carbon nanotubes (MWCNTs) under external radial pressure is studied on the base of a multiple-shell model. The modified Mushtari-Donell-Vlasov type equations taking into account the van der Waals (vdW) interaction forces between adjacent tubes are used as the governing ones. In contrast to a majority of available studies on buckling of MWCNTs, which consider only the simply supported boundary conditions, this paper based on the asymptotic approach allows for the study of the buckling behavior of MWCNTs with different variants of the boundary conditions at the tube edges. At first, the pre-buckling membrane hoop stress-resultants induced by radial pressure are determined for each wall. Then, introducing a small parameter defined as a thickness-to-radius ratio, the asymptotic solutions of the boundary value problem are constructed for different cases which depend on the outermost radius of a MWCNT. The relevance of the present approach is confirmed by good agreement between asymptotic estimates and exact values of the buckling radial pressure for simply supported double-and triple-walled nanotubes determined on the base of the accepted shell model. In addition, the validity of the asymptotic estimates is justified by comparing theirs with existing data obtained on the base of the available multiple-shell model taking into account the pressure dependence of the interlayer vdW forces. The influence of the outermost radius, aspect ratio and boundary conditions as well on the buckling radial pressure is analyzed in this study.

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Section: On Applicability Of the Shell Theory For Short Carbon Nanotubesmentioning

confidence: 93%

“…So, S.A. Fazelzadeh et al. showed that the effect of nonlocal parameter on the natural frequencies is significant only for SWCNTs with a very low aspect ratio and a small diameter. And M. Strozzi et al.…”

Section: On Applicability Of the Shell Theory For Short Carbon Nanotubesmentioning

confidence: 99%

Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

Mikhasev

Ботогова

2016

Z Angew Math Mech

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“…We can realize that the initial state of Zn3d 9 is odd symmetry, but the initial state of Zn3d 10 L shows even symmetry. The different spatial symmetry of Zn3d 9 and Zn3d 10 L originated from different force [14]. The external fields on earth just gravitational field, magnetic field and electric field can be considered.…”

Section: The Spatial Symmetry Of Excited Zinc Filmmentioning

confidence: 99%

Charge Transfer Mechanism and Spatial Density Correlation of Electronic States of Excited Zinc (3d<sup>9</sup>) Films

Chen¹,

Hamasaki²,

Manaka³

et al. 2014

OJPC

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In material science, half filled 3d orbital of transition metals is essentially an important factor controlling characteristics of alloys and compounds. This paper presents a result of the challenge of excitation of inner-core electron system with long lifetime of zinc films. The advanced zinc films with excited inner-core electron, 3d n (n = 9, 8). We report experimental results of XPS measurements of 9 points in the sample along vertical direction, respectively. The most pronounced futures are existence of satellites, which are about 4 eV higher than the main lines. According to the charge transfer mechanism proposed by A. Kotani and K. Okada, it was clarified that the origins of these peaks are c3d 9 L for the main peak and c3d 9 for the satellite, respectively. From the energy difference, δE B , and peak intensity ratio, I + /I − , between c3d 9 and c3d 10 L, the energy for charge transfer, ∆, and mixing energy, T, were estimated. In the region where the intensity of c3d 10 L becomes large, ∆ becomes small, 1.2 < ∆ < 2.7, and T becomes small, too, 0.1 < T < 0.9, respectively. In this calculation, we supposed U dc = 5.5 eV and U dd = 5.5 eV. In the analysis along vertical direction, intensity profile of Zn3d 9 showed odd functional symmetry and that of Zn3d 10 L showed even functional symmetry. Only the intensity profile of C1s (288 eV) showed the same spatial correlation with Zn3d 9 . In our experiment, the sample also showed high mobility of the constituting elements. These suggest that charge conservation in excited zinc atom suggests combination between Zn3d 9 and C 2− .

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“…In recent years, in order to obtain more realistic responses, the nanoscale orthotropic shell was introduced where, in this model, the nanoscale effects are measured based on nonlocal theory. 44 It can be said that in previous studies, conducted on CNT, the effects of size dependency, anisotropy, shear effects, and CNT cylindrical shape have rarely been simultaneously considered. For the first time, the present work develops a new model of chirality-dependent vibration of the anisotropic CNT based on couple stress theory.…”

Section: Introductionmentioning

confidence: 99%

“…By modeling the zigzag CNTs as a nonlocal Levinson beam model, Maachou et al 43 studied the vibration behavior of CNTs under thermal effects. Fazelzadeh and Ghavanloo,44,45 using the anisotropic nonlocal cylindrical shell model, investigated the effects of various parameters on CNTs frequency. Besides, they studied the effect of chirality on CNT vibrations.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Beni

Mehralian

Zeverdejani

2017

Journal of Low Frequency Noise, Vibration and Active Control

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In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.

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Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality

Cited by 72 publications

References 39 publications

Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

Charge Transfer Mechanism and Spatial Density Correlation of Electronic States of Excited Zinc (3d<sup>9</sup>) Films

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

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Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality

Cited by 72 publications

References 39 publications

Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

Charge Transfer Mechanism and Spatial Density Correlation of Electronic States of Excited Zinc (3d&lt;sup&gt;9&lt;/sup&gt;) Films

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

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Charge Transfer Mechanism and Spatial Density Correlation of Electronic States of Excited Zinc (3d<sup>9</sup>) Films