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M. Di Paola, R. Heuer, A. Pirrotta:
"Mechanical behavior of fractional visco-elastic beams";
Talk: 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Wien; 2012-09-10 - 2012-09-14.

Aim of this paper is the response evaluation of fractional visco-elastic Euler-Bernoulli beam under quasi-static loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is derived that, for homogeneous beam without assigned displacements or visco-elastic constraints, the bending moment and shear distribution along the beam does not depend on time and thus equals the bending moment and shear distribution of the purely elastic case. Thus the so-called correspondence principle also holds in the case of fractional visco-elasticity.

fractional calculus, visco-elastic beam, quasi-static problems, virtual work principle