Fractional Euler-Bernoulli Beam Theory Based on the Fractional Strain-Displacement Relation and its Application in Free Vibration, Bending and Buckling Analyses of Micro/Nanobeams
Zaher Rahimia, Samrand Rash Ahmadia, W. Sumelkab
aMechanical Engineering Department, Urmia University, Urmia, Iran
bPoznan University of Technology, Institute of Structural Engineering, Piotrowo 5, 60-965 Poznan, Poland
Received: May 12, 2018; in final form July 4, 2018
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Applications of fractional calculus in the constitutive relation lead to the fractional derivatives models. They are stately generalization of the integer derivatives models - this general form makes fractional derivatives models more flexible and suitable to describe properties and behavior of different materials/structures. In the present work, the general strain deformation gradient has been presented by using the modified conformable fractional derivatives definition. Within this approach the fractional Euler-Bernoulli beam theory has been formulated and applied to the analysis of free vibration, bending and buckling of micro/nanobeams which exhibit strong scale effect.

topics: fractional derivatives model, fractional Euler-Bernoulli theory, free vibration, bending, buckling, nanobeam