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Modelling One-Dimensional Fractional Impact Using Basic Fractional Viscoelastic Models

[+] Author Affiliations
Arman Dabiri, Eric A. Butcher, Morad Nazari

University of Arizona, Tucson, AZ

Paper No. DETC2016-60339, pp. V006T09A064; 8 pages
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5018-3
  • Copyright © 2016 by ASME


Viscoelastic materials can be mathematically represented using integer- or order models. It has been shown in different studies that modeling a viscoelastic material usually requires an enormous number of parameters. Fractional viscoelastic models have been shown to be advantageous over integer viscoelastic models in the representation of viscoelastic materials, specifically when the system has memory or hereditary property. However, to the authors’ knowledge, no study has yet been done about fractional impact models. Thus, in this paper, fractional modified Kelvin-Voigt model and fractional Maxwell model are introduced as one-dimensional fractional impact models for basic fractional viscoelastic materials. The force-displacement hysteresis curves are obtained by using the fractional Chebyshev collocation method and the gradient of impact force, penetration depth, separation depth, and the coefficient of restitution are studies. It is shown numerically that fractional viscoelastic models behave more realistic than their integer counterparts in one-dimensional impact problems.

Copyright © 2016 by ASME
Topics: Modeling



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