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Article

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Title

Investigation of Free Vibration and Buckling of Timoshenko Nano-beam Based on a General Form of Eringen Theory Using Conformable Fractional Derivative and Galerkin Method

Authors

[ 1 ] Instytut Konstrukcji Budowlanych, Wydział Budownictwa i Inżynierii Środowiska, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.7] Civil engineering and transport

Year of publication

2019

Published in

Engineering Transactions

Journal year: 2019 | Journal volume: vol. 67 | Journal number: no. 3

Article type

scientific article

Publication language

english

Keywords
EN
  • fractional calculus
  • nonlocal fractional derivative model
  • free vibration
  • Timoshenko beam
  • Galerkin method
  • buckling
Abstract

EN The purpose of this paper is to study the free vibration and buckling of a Timoshenko nano-beam using the general form of the Eringen theory generalized based on the fractional derivatives. In this paper, using the conformable fractional derivative (CFD) definition the generalized form of the Eringen nonlocal theory (ENT) is used to consider the effects of integer and noninteger stress gradients in the constitutive relation and also to consider small-scale effect in the vibration of a Timoshenko nano-beam. The governing equation is solved by the Galerkin method. Free vibration and buckling of a Timoshenko simply supported (S) nano-beam is investigated, and the influence of the fractional and nonlocal parameters is shown on the frequency ratio and buckling ratio. In this sense, the obtained formulation allows for an easier mapping of experimental results on nano-beams. The new theory (fractional parameter) makes the modeling more flexible. The model can conclude all of the integer and non-integer operators and is not limited to the special operators such as ENT. In other words, it allows to use more sophisticated/flexible mathematics to model physical phenomena.

Pages (from - to)

347 - 367

DOI

10.24423/EngTrans.1001.20190426

URL

http://et.ippt.gov.pl/index.php/et/article/view/1001

License type

CC BY-SA (attribution - share alike)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Full text of article

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Access level to full text

public

Ministry points / journal

20

Ministry points / journal in years 2017-2021

70

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