Investigation of Free Vibration and Buckling of Timoshenko Nano-beam Based on a General Form of Eringen Theory Using Conformable Fractional Derivative and Galerkin Method

Farogh Soufi MOHAMMADI, Zaher RAHIMI, Wojciech SUMELKA & Xiao-Jun YANG
The purpose of this paper is to study the free vibration and buckling of a Timoshenko nano-beam using the general form of the Eringen theory generalized based on the fractional derivatives. In this paper, using the conformable fractional derivative (CFD) definition the generalized form of the Eringen nonlocal theory (ENT) is used to consider the effects of integer and noninteger stress gradients in the constitutive relation and also to consider small-scale effect in the vibration...
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