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On the application of fractional calculus for the formulation of viscoelastic Reddy beam

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Abstract

The focus of the current work is to present the bending analysis of visco-elastic beams based on Reddy’s third-order shear deformation theory. Fractional calculus is taken into account for dealing with the fractional derivative terms, able to better describe the damping behaviour of any visco-elastic material. Numerical analyses of beams with different boundary conditions have been proposed and discussed following two different approaches, namely the finite element method and the Galerkin method. An assessment of the proposed approach is presented by comparing the computed solutions with those obtained with the classical and first-order shear deformation theories available in the literature.

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Authors and Affiliations

  1. Departments of Engineering, University of Palermo, Viale delle Scienze 8, Palermo, Italy

    M. Di Paola

  2. Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77843-3123, USA

    J. N. Reddy

  3. Department of Engineering, University of Campania “L. Vanvitelli”, Via Roma 29, Aversa, CE, Italy

    E. Ruocco

Authors
  1. M. Di Paola
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  2. J. N. Reddy
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  3. E. Ruocco
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Correspondence to E. Ruocco.

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Di Paola, M., Reddy, J.N. & Ruocco, E. On the application of fractional calculus for the formulation of viscoelastic Reddy beam. Meccanica 55, 1365–1378 (2020). https://doi.org/10.1007/s11012-020-01177-3

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  • DOI: https://doi.org/10.1007/s11012-020-01177-3

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