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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

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

Rahimi Z., Sumelka W., Shafiei S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

Vol. 66, nr 5

737--745

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.