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

Abstract

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.