Timoshenko vs Euler-Bernoulli beam: fractional visco-elastic behaviour

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Abstract

The Euler-Bernoulli beam theory is well established in such a way that engineers arevery confident with the determination of stress field or deflections of the elastic beam based onthis theory. Conversely Timoshenko theory is not so much used by engineers. However in suchcases Euler-Bernoulli theory that neglects the effect of transversalshear deformation leads tounacceptable results. For instance when dealing with the visco-elastic behaviour the sheardeformations play a fundamental role. Recent studies [1]-[2] on the response evaluation of visco-elastic Euler-Bernoulli beam under quasi-static and dynamic loads, have been stressed that for better capturing the visco-elastic behavior a fractional constitutive law has to be considered. In thiscontext it has been provided that, for homogeneous beam both correspondence principles also hold,then the study of a fractional visco-elastic Euler-Bernoulli beam may be derived from the elastic one.As aforementioned in dealing with visco-elasticity the Timoshenko beam model is more properthan Euler-Bernoulli’s one, thenthis paper provides important informationsto engineeringdesigners, introducing exact linking relationships between visco-elastic Euler-Bernoulli beam solutions and visco-elastic Timoshenkobeam solutions. Thus the effect of transverse shear deformations may be taken into account for, without the need of a studying a more complicated model.
Original languageEnglish
Number of pages10
Publication statusPublished - 2013

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