On the Euler-Bernoulli anel Timoshenko-Ehrenfest beam theories under fractional calculus approach

Abstract

General fractional solutions for the Euler-Bernoulli and Timoshenko-Ehrenfest differential equations are deduced for the case of a simply supported beam submitted to uniformly  distributed static load. Both solutions are confronted against Ansys software results, taken as reference, leading to the corresponding particular fractional solutions. As expected, both particular solutions converge to the Ansys results for small deflections and beam with high-aspect ratio, while, for opposite geometrical features, the fractional Timoshenko-Ehrenfest solution performs slightly better, kept the linear elasticity. The shear effects are realized in the fractional order transformation of the Euler-Bernoulli model; besides, from comparative analysis, other physical effects in the strueture may be present in the fractional order.