Three dimensional vibration and bending analysis of carbon nanotubes embedded in elastic medium based on theory of elasticity

Alibeigloo, A.; Shaban, M.

doi:10.1590/s1679-78252014001200002

Cited by 12 publications

(2 citation statements)

References 32 publications

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“…Akgöz ve Civalek [15] used modified couple stress and strain gradient elasticity theories for bending analysis of SWCNTs. Shaban and Alibeigloo [16] investigated the free vibration and bending behavior of SWCNTs embedded in an elastic medium by using on three-dimensional theory of elasticity. Wu et al [17] investigated the surface and nonlocal elasticity effects on the elastic behavior of bending nanowires.…”

Section: Introductionmentioning

confidence: 99%

Bending of CNTs Under The Partial Uniform Load

Arda¹,

Aydoğdu²

2016

International Journal of Engineering &Amp; Applied Sciences

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Section: Introductionmentioning

confidence: 99%

Bending of CNTs Under The Partial Uniform Load

Arda¹,

Aydoğdu²

2016

International Journal of Engineering &Amp; Applied Sciences

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“…Deng and Yang [35] studied vibration of fluid filled multiwall carbon nanotubes using nonlocal Flugge shell model. A rare approach of three dimensional vibrational and bending analysis was performed by Shaban and Alibeigloo [36] by taking nonlocal shell model to account for the size effect.…”

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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