Nano- and viscoelastic Beck’s column on elastic foundation

Abstract

Beck’s type column on a Winkler type foundation is the subject of the present analysis. Instead of the Bernoulli–Euler model describing the rod, two generalized models will be adopted: Eringen’s nonlocal model corresponding to nano-rods and a viscoelastic model of fractional Kelvin–Voigt type. The analysis shows that for a nano-rod the Herrmann–Smith paradox holds whilst for a viscoelastic rod it does not.

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Correspondence to Dusan Zorica.

Additional information

This research is supported by the Serbian Ministry of Education and Science project 174005, as well as by the Secretariat for Science of Vojvodina project 114 − 451 − 1084.

Yanni Bouras acknowledges Victoria University for the financial support provided for travel expenses.

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Atanackovic, T.M., Bouras, Y. & Zorica, D. Nano- and viscoelastic Beck’s column on elastic foundation. Acta Mech 226, 2335–2345 (2015). https://doi.org/10.1007/s00707-015-1327-1

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Keywords

  • Critical Load
  • Fractional Derivative
  • Elastic Foundation
  • Viscoelastic Model
  • Critical Force