Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

Ciğeroğlu, Ender; Samandari, Hamed

doi:10.1016/j.physe.2014.07.010

Cited by 26 publications

(5 citation statements)

References 37 publications

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“…Applying the asymptotic expansion and multiple scales analytical method to the general solutions (22)(23), the following two equations of motion can be obtained [10]…”

Section: Methodsmentioning

confidence: 99%

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Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes

Strozzi

Смірнов

Manevitch

et al. 2016

Journal of Sound and Vibration

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“…Applying the asymptotic expansion and multiple scales analytical method to the general solutions (22)(23), the following two equations of motion can be obtained [10]…”

Section: Methodsmentioning

confidence: 99%

“…Other relevant studies on CNTs nonlinear vibrations and instability can be found in Refs. [18][19][20][21][22][23][24][25][26][27][28].…”

Section: Manevitch and Musienkomentioning

confidence: 99%

Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes

Strozzi

Смірнов

Manevitch

et al. 2016

Journal of Sound and Vibration

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“…Cigeroglu and Samandari [48] studied nonlinear free vibrations of DWCNTs embedded in an elastic medium. Geometric nonlinearities due to large deflection of SWCNTs and nonlinear van der Waals interaction forces were considered.…”

mentioning

confidence: 99%

Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces

Strozzi¹,

Смірнов²,

Pellicano³

et al. 2022

International Journal of Non-Linear Mechanics

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“…A similar study was performed by Sadri et al [49] with the surrounding medium being modeled as Winkler type model. Cigeroglu and Samandari [50] employed differential quadrature method to perform yet another similar study. Ambrosini and Borbon [51] studied the influence of van der Waals interaction coefficient on the vibrations of double-walled carbon nanotubes using higher order beam model.…”

Section: Literature Reviewmentioning

confidence: 99%

An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

Khan¹

2021

Preprint

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Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

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Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

Cited by 26 publications

References 37 publications

Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes

Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes

Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces

An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

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