Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

Arman Dabiri, Eric Butcher, Morad Nazari

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

Original languageEnglish (US)
Pages (from-to)230-244
Number of pages15
JournalJournal of Sound and Vibration
StatePublished - Feb 3 2017


  • Caputo
  • Coefficient of restitution
  • Compliant contact model
  • Continuous contact force model
  • Fractional Chebyshev collocation method
  • Fractional order system
  • Grunwald–Letnikov
  • Impact
  • Kelvin–Voigt model
  • Materials with memory
  • Maxwell model
  • Riemann–Liouville
  • Standard linear solid model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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