Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method

Payam Soltani; Anoshirvan Farshidianfar

doi:10.1016/j.apm.2011.11.002

Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method

Payam Soltani, Anoshirvan Farshidianfar

Ferdowsi University of Mashhad

Research output: Contribution to journal › Article › peer-review

53 Citations (Scopus)

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Abstract

A nonlinear model is developed for the vibration of a single-walled carbon nanotube (SWCNT) based on Eringen’s nonlocal elasticity theory. The nanotube is assumed to be embedded in a Pasternak-type foundation with simply supported boundary conditions. The nonlinear equation of motion is solved by the energy balance method (EBM) to obtain a sufficiently accurate flow-induced frequency. It is demonstrated that the nonlinearity of the model makes a reasonable change to the frequency at high flow velocity and for the large deformations. Furthermore, the deviation of the frequency from the linear frequency will be exaggerated with an increase in the nonlocal parameter and a decrease of the Pasternak parameters. Ultimately, the results show that the nonlinearity of the model can be effectively tuned by applying axial tension to the nanotube.

Original language	English
Pages (from-to)	3712-3724
Number of pages	13
Journal	Applied Mathematical Modelling
Volume	36
Issue number	8
Early online date	10 Nov 2011
DOIs	https://doi.org/10.1016/j.apm.2011.11.002
Publication status	Published - Aug 2012

Bibliographical note

© 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

Flow-induced vibration
Nonlinear vibration
Energy balance method
Nonlocal theory
Pasternak foundation

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Cite this

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title = "Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method",

abstract = "A nonlinear model is developed for the vibration of a single-walled carbon nanotube (SWCNT) based on Eringen{\textquoteright}s nonlocal elasticity theory. The nanotube is assumed to be embedded in a Pasternak-type foundation with simply supported boundary conditions. The nonlinear equation of motion is solved by the energy balance method (EBM) to obtain a sufficiently accurate flow-induced frequency. It is demonstrated that the nonlinearity of the model makes a reasonable change to the frequency at high flow velocity and for the large deformations. Furthermore, the deviation of the frequency from the linear frequency will be exaggerated with an increase in the nonlocal parameter and a decrease of the Pasternak parameters. Ultimately, the results show that the nonlinearity of the model can be effectively tuned by applying axial tension to the nanotube.",

keywords = "Flow-induced vibration, Nonlinear vibration, Energy balance method, Nonlocal theory, Pasternak foundation",

author = "Payam Soltani and Anoshirvan Farshidianfar",

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AU - Farshidianfar, Anoshirvan

N1 - © 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

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N2 - A nonlinear model is developed for the vibration of a single-walled carbon nanotube (SWCNT) based on Eringen’s nonlocal elasticity theory. The nanotube is assumed to be embedded in a Pasternak-type foundation with simply supported boundary conditions. The nonlinear equation of motion is solved by the energy balance method (EBM) to obtain a sufficiently accurate flow-induced frequency. It is demonstrated that the nonlinearity of the model makes a reasonable change to the frequency at high flow velocity and for the large deformations. Furthermore, the deviation of the frequency from the linear frequency will be exaggerated with an increase in the nonlocal parameter and a decrease of the Pasternak parameters. Ultimately, the results show that the nonlinearity of the model can be effectively tuned by applying axial tension to the nanotube.

AB - A nonlinear model is developed for the vibration of a single-walled carbon nanotube (SWCNT) based on Eringen’s nonlocal elasticity theory. The nanotube is assumed to be embedded in a Pasternak-type foundation with simply supported boundary conditions. The nonlinear equation of motion is solved by the energy balance method (EBM) to obtain a sufficiently accurate flow-induced frequency. It is demonstrated that the nonlinearity of the model makes a reasonable change to the frequency at high flow velocity and for the large deformations. Furthermore, the deviation of the frequency from the linear frequency will be exaggerated with an increase in the nonlocal parameter and a decrease of the Pasternak parameters. Ultimately, the results show that the nonlinearity of the model can be effectively tuned by applying axial tension to the nanotube.

KW - Flow-induced vibration

KW - Nonlinear vibration

KW - Energy balance method

KW - Nonlocal theory

KW - Pasternak foundation

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DO - 10.1016/j.apm.2011.11.002

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JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

IS - 8

ER -

Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method

Abstract

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Keywords

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