2016
DOI: 10.21467/jmm.3.1.9-13
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Carbon Nanotube Structure Vibration Based on Non-local Elasticity

Abstract: A B S T R A C TThis manuscript investigates the bending vibration dynamic of a single walled carbon nanotube (SWCNT) based on the theory of non-local elasticity. Fundamental natural frequencies and mode shapes of the SWCNT are computed by using a semi-analytical procedure called differential quadrature method (DQM), which gives accurate results in reference with the exact solution.

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Cited by 12 publications
(15 citation statements)
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“…Carbon nanotubes (CNTs) [3] are nanoscale structures made of pure carbon that are long and thin and shaped like tubes, these molecules are same sized and structured in chemical boding and aligned by Van der Walls forces into ropes, the length of CNTs can reach some millimeters while its diameter in on the order of some nanometers. In reference to the number of structured walls, we can distinguish single walled nanotubes (SWCNTs) shown in Figure.2, and multi-walled nanotubes (MWNTs) depending upon the walls number.…”
Section: Carbon Nanotubesmentioning
confidence: 99%
“…Carbon nanotubes (CNTs) [3] are nanoscale structures made of pure carbon that are long and thin and shaped like tubes, these molecules are same sized and structured in chemical boding and aligned by Van der Walls forces into ropes, the length of CNTs can reach some millimeters while its diameter in on the order of some nanometers. In reference to the number of structured walls, we can distinguish single walled nanotubes (SWCNTs) shown in Figure.2, and multi-walled nanotubes (MWNTs) depending upon the walls number.…”
Section: Carbon Nanotubesmentioning
confidence: 99%
“…and Zamanian et al [22]. In some further studies, Abdel-Rahman and Nayfeh [23], Hawwa and Al-Qahtani [24], Hajnayeb and Khaden [25] and Belhadj et al [26] presented different works on the vibration and instability of DWCNTs under the influence of electrostatic actuations. In the later work, a DWCNT was situated and conditioned to a direct and alternating voltage and different behaviours of the nanotubes were recorded as the exciting agent was varied.…”
Section: Introductionmentioning
confidence: 99%
“…It was concluded that both walls have the same frequency of vibration under the two resonant conditions considered. In another work, Belhadj et al [26] examined the vibration behaviour of a simply supported SWCNT employing the nonlocal theory of elasticity. The authors obtained the natural frequency up to third mode while they also established high level of frequency.…”
Section: Introductionmentioning
confidence: 99%
“…In an earlier work, Zamanian et al [22] presented the non-linear vibrations analysis of a microresonator subjected to piezoelectric and electrostatic actuations. As a continuation of the tremendous work, Abdel-Rahman, Hawwa, Hajnayeb, and Belhadj [23][24][25][26] performed a vibration and instability studies of DWCNT using a nonlinear model and considering an electrostatic actuation as an external excitation agent. In their work, a DWCNT was situated and conditioned to a direct and alternating voltage and different behaviors of the nanotubes were recorded as the exciting agent is varied.…”
Section: Introductionmentioning
confidence: 99%
“…They went further to determine the bifurcation point of the DWCNT and concluded that both walls have the same frequency of vibration under the two resonant conditions considered. Belhadj et al [26] carried out the vibration analysis of a pinned-pinned supported SWCNT employing nonlocal theory of elasticity and obtained natural frequency up to third mode. The authors also put forward an explanation on the advantages of the high frequency obtained in their work to optical applications.…”
Section: Introductionmentioning
confidence: 99%