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M. Di Paola, R. Heuer, A. Pirrotta:
"Fractional visco-elastic Euler-Bernoulli beam";
International Journal of Solids and Structures, 50 (2013), 3505 - 3510.

Aim of this paper is the response evaluation of fractional visco-elastic Euler-Bernoulli beam under quasistatic
and dynamic 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 shown that, for homogeneous beam both correspondence
principles also hold in the case of Euler-Bernoulli beam with fractional constitutive law. Virtual
work principle is also derived and applied to some case studies.

Fractional calculus, Visco-elastic beam, Euler-Bernoulli beam, Quasi-static problems, Virtual work principle

http://dx.doi.org/10.1016/j.ijsolstr.2013.06.010