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Tytuł artykułu

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

Treść / Zawartość
Identyfikatory
Warianty tytułu
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.
Rocznik
Strony
737--745
Opis fizyczny
Bibliogr. 39 poz., tab., wykr.
Twórcy
autor
  • Mechanical Engineering Department, Urmia University, Urmia, Iran
autor
  • Poznan University of Technology, Institute of Structural Engineering, Piotrowo 5 Street, 60-965 Poznan, Poland
autor
  • Mechanical Engineering Department, Tabriz University, Tabriz, Iran
Bibliografia
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  • [19] Pálfalvi, A. Efficient solution of a vibration equation involving fractional derivatives. International Journal of Non-Linear Mechanics, 45(2), pp. 169‒175, 2010.
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  • [22] W. Sumelka, R. Zaera, and J. Fernández-Sáez, A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics, Meccanica, 50, 9, pp. 2309‒2323, 2015.
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  • [32] Nazemnezhad, R. and Hosseini-Hashemi, S. Non-local nonlinear free vibration of functionally graded nanobeams. Composite Structures, 110, pp. 192‒199, 2014.
  • [33] Rahimi, Z., Sumelka, W., and Yang, Xiao-Jun. Linear And Non-Linear Free Vibration Of Nano Beams Based On A New Fractional Non-Local Theory, Engineering Computations, 34 (5), pp. 1754 -1770, 2017.
  • [34] Abbasnejad, B., Rezazadeh, G., and Shabani, R. Stability analysis of a capacitive fgm micro-beam using modified couple stress theory. Acta Mechanica Solida Sinica, 26(4), pp. 427‒440, 2013.
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  • [36] Z. Rahimi, G. Rezazadeh, W. Sumelka, and X.-J. Yang. A study of critical point instability of micro and nano beams under a distributed variable-pressure force in the framework of the fractional non-linear nonlocal theory. Archives of Mechanics, 69, 6, pp. 413–433, 2017.
  • [37] Pecherski, R.B. Macroscopic measure of the rate of deformation produced by micro-shear banding. Archives of Mechanics, 49(2), pp. 385‒40, 1997.
  • [38] Vasily E. Tarasov, Local Fractional Derivatives of Differentiable Functions are Integer-order Derivatives or Zero, International Journal of Applied and Computational Mathematics, 2(2), pp. 195–201, 2016.
  • [39] R. Almeida, M. Guzowska, and T. Odzijewicz, A remark on local fractional calculus and ordinary derivatives, Open Mathematics, 14, pp. 1122–1124, 2016.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5882829f-cd62-42a8-bbde-886bee164c98
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