The analysis of non-linear free vibration of FGM nano-beams based on the conformable fractional non-local model

• Autorzy: Rahimi Z. , Sumelka W. , Shafiei S.

Identyfikatory

DOI

10.24425/bpas.2018.125341

• Języki publikacji: EN

Abstrakty

EN

Continuum models generalized by fractional calculus are used in different mechanical problems. In this paper, by using the conformable fractional derivative (CFD) definition, a general form of Eringen non-local theory as a fractional non-local model (FNM) is formulated. It is then used to study the non-linear free vibration of a functional graded material (FGM) nano-beam in the presence of von-Kármán non-linearity. A numerical solution is obtained via Galerkin and multiple scale methods and effects of the integer and non-integer (fractional) order of stress gradient (in the non-local stress-strain relation) on the ratio of the non-local non-linear natural frequency to classical non-linear natural frequency of simply-supported (S-S) and clamped-free (C-F) FGM nano-beams are presented.

Słowa kluczowe

EN

FGM nano beam; nonlinear free vibration; fractional calculus; integer stress; non-integer stress; gradient’s order; fractional non-local model

PL

rachunek różniczkowy; FGM; drgania swobodne

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 5
• Strony: 737--745
• Opis fizyczny: Bibliogr. 39 poz., tab., wykr.

Twórcy

autor

Rahimi Z.

• Mechanical Engineering Department, Urmia University, Urmia, Iran

autor

Sumelka W.

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

autor

Shafiei S.

• Mechanical Engineering Department, Tabriz University, Tabriz, Iran

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).