6533b861fe1ef96bd12c4231

RESEARCH PRODUCT

Fractional visco-elastic Timoshenko beam deflection via single equation

Salvatore LorenzoStefano CutronaAlberto Di MatteoAntonina PirrottaAntonina Pirrotta

subject

Timoshenko beam theoryNumerical AnalysisMellin transformDifferential equationDeflection (engineering)Applied MathematicsMathematical analysisGeneral EngineeringFinite differenceTime domainViscoelasticityFractional calculusMathematics

description

SUMMARY This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letnikov approximation of the fractional derivative. Moreover, Timoshenko beam response is generally evaluated by solving a couple of differential equations. In this paper, expressing the equation of the elastic curve just through a single relation, a more general procedure, which allows the determination of the beam response for any load condition and type of constraints, is developed. Copyright © 2015 John Wiley & Sons, Ltd.

yearjournalcountryeditionlanguage
2015-06-10International Journal for Numerical Methods in Engineering
https://doi.org/10.1002/nme.4956