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

Fatahi-Vajari, Alireza; Azimzadeh, Z.; Hussain, Muzamal

doi:10.1049/mnl.2019.0203

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…Here, Galerkin’s method is used to solve the CNT problem of differential equations in an efficient and comprehensive way [71–79]. The analysis of vibration of SWCNTs as a theoretical work is very necessary before their practical applications.…”

Section: Theoretical Formulationsmentioning

confidence: 99%

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Hussain

2020

Jnl of Sandwich Structures & Materials

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Carbon nanotubes fascinate new materials with astonishing mechanical, optical, and electrical properties. In fact, carbon nanotubes are kinds of rolled graphene sheets, and the rolling manner shows the basic properties of the tube, and that is actually the main reason for the extraordinary feature of the carbon nanotubes. This paper aims to presents formulation of Love’s shell theory for single-wall carbon nanotubes (SWCNTs) using Galerkin’s method. For this system, the governing equation is developed with proposed method. It is assumed that C–C and C–F support conditions are applied on the edge of carbon nanotube. Zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different mode and in-plane rigidity with end conditions. Moreover, the influence of mass density per unit lateral area on the same structure is also developed. It is also concluded that the fundamental frequencies of chiral tubes are lower than that of zigzag tubes frequencies. By increasing values of in-plane rigidity, resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. Though the trends of frequency values of both mass density per unit lateral area and in-plane rigidity are converse to each other. It is shown that variation in mass density has a significant effect on the vibration of SWCNTs. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used. Tube dynamical equations for the present problem are taken in the integral form energy expressions for a carbon nanotube. The axial modal deformations are approximated by making use of the beam functions. The proposed model is continuum-model for getting the dynamic character of SWCNTs and to validate the results by earlier methods.

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Section: Theoretical Formulationsmentioning

confidence: 99%

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Hussain

2020

Jnl of Sandwich Structures & Materials

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“…Due to the importance of carbon nanotubes (CNT), which are known as the strongest materials today, various studies are carried out about composites that contains CNT. Up to now, several researches have been done on the studying of carbon nanotubes as can be seen from the examples of [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Dispersion relation for transverse waves in pre-stressed irregular single-walled carbon nanotubes

Selim

2020

Phys. Scr.

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This article studies the dispersion relation of transverse waves in an initially stresses single-walled carbon nanotube (SWCNT) with surface irregularity using Flügge shell theory. Taking into account the effects of surface irregularity and initial stresses, propagation of transverse waves is studied and dispersion curves are plotted for optical transverse waves in several figures. The effects of surface irregularity and initial stresses are confirmed by comparing obtained numerical results with those in cases of uniform and initial stress–free SWCNT. Obtained results turn out that, the increase of irregularity parameter increases the phase velocity of transverse waves, while the increase of the initial stress parameter decreases the phase velocity of transverse waves propagating in SWCNTs. To the author best knowledge, effects of surface irregularity and initial stresses on transverse waves propagation, especially propagation in single-walled carbon nanotubes, have not been done before. The previous studies were devoted to the uniform and initial stresses-free carbon nanotubes. It should be emphasized that the transverse waves propagation in pre-stressed and irregular single-walled carbon nanotubes is novel, workable, and at the beginning of the path. İn this manner, understanding the influences of surface irregularity as well as initial stresses on the phase velocity of transverse waves may serve as useful references for the applications and designs of nano oscillators and nanodevices, in which single-walled carbon nanotubes act as the most prevalent nanocomposite structural element.

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Vibration of initially stressed nonlocal irregular nanoplate using wave propagation approach

Selim

Gepreel

Mohammed

et al. 2022

Waves in Random and Complex Media

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

Cited by 5 publications

References 31 publications

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Dispersion relation for transverse waves in pre-stressed irregular single-walled carbon nanotubes

Vibration of initially stressed nonlocal irregular nanoplate using wave propagation approach

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