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

• Autorzy: Mohammadi Farogh Souf , Rahimi Zaher , Sumelka Wojciech , Yang Xiao-Jun
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

fractional calculus; nonlocal fractional derivative model; free vibration; Timoshenko beam; Galerkin method; buckling

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2019
• Tom: Vol. 67, iss. 3
• Strony: 347--367
• Opis fizyczny: Bibliogr. 48 poz., tab., wykr.

Twórcy

autor

Mohammadi Farogh Souf

• Mechanical Engineering Department, Urmia University Urmia, Iran

autor

Rahimi Zaher

• Mechanical Engineering Department, Urmia University Urmia, Iran

autor

Sumelka Wojciech

• Institute of Structural Engineering, Poznan University of Technology Piotrowo 5, 60-965 Poznan, Poland

autor

Yang Xiao-Jun

• School of Mechanics and Civil Engineering China University of Mining and Technology Xuzhou 221116, China
• State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and Technology Xuzhou 221116, China

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).