Fractional visco-elastic Timoshenko beam from elastic Euler-Bernoulli beam

The Euler-Bernoulli beam theory is well established in such a way that engineers are veryconfident with the determination of stress field or deflections of the elastic beam based on thistheory. Conversely Timoshenko theory is not so much used by engineer freelancers. However insuch cases Euler-Bernoulli theory, that neglects the effect of transversal shear deformation leads tounacceptable results. For instance when dealing with the visco-elastic behavior, sheardeformations play a fundamental role. Recent studies on the response evaluation of visco-elasticEuler-Bernoulli beam under quasi-static and dynamic loads, have been stressed that, for bettercapturing the visco-elastic behavior, a fractional constitutive law has to be considered. In thiscontext it has been provided that, for homogeneous beam correspondence principle also holds,then the study of a fractional visco-elastic Euler-Bernoulli beam may be derived from the elasticone. As aforementioned in dealing with visco-elasticity the Timoshenko beam model is moreproper than Euler-Bernoulli’s one, then this paper provides important information to engineeringdesigners, introducing exact linking relationships between elastic Euler-Bernoulli beam responseand fractional visco-elastic Timoshenko beam response. The ready-to-use tables andstraightforward formulation have been provided leading to tremendous cost analysis savings andimproved quality.