Mathematics (Feb 2022)

Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams

  • Francesco Paolo Pinnola,
  • Raffaele Barretta,
  • Francesco Marotti de Sciarra,
  • Antonina Pirrotta

DOI
https://doi.org/10.3390/math10030477
Journal volume & issue
Vol. 10, no. 3
p. 477

Abstract

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A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be useful for the design and optimization of small-scale devices exhibiting flexural behaviour.

Keywords