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Analytical Modelling and Experimental Identification of Viscoelastic Mechanical Systems

  • Giuseppe Catania
  • Silvio Sorrentino

In the present study non-integer order or fractional derivative rheological models are applied to the dynamical analysis of mechanical systems.

Keywords

Fractional Calculus Relaxation Modulus Creep Compliance Derivative Model Fractional Derivative Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Catania G, Sorrentino S (2005) Experimental identification of a fractional derivative linear model for viscoelastic materials, Long Beach, California, Proceedings of IDETC/CIE 2005 (DETC 2005-85725).Google Scholar
  2. 2.
    Frammartino D (2000) Modelli analitici evoluti per lo studio di sistemi smorzati, Degree thesis, Politecnico di Torino (in Italian).Google Scholar
  3. 3.
    Jones DG (2001) Handbook of Viscoelastic Vibration Damping. Wiley, New York.Google Scholar
  4. 4.
    Caputo M, Mainardi F (1971) Linear models of dissipation in anelastic solids, Rivista del Nuovo Cimento 1:161-198.CrossRefGoogle Scholar
  5. 5.
    Mainardi F (1997) Fractional calculus: some basic problems in continuum and statistical mechanics, in: Fractals and Fractional Calculus in Continuum Mechanics. Springer, New York.Google Scholar
  6. 6.
    Beyer H, Kempfle S (1995) Definition of physically consistent damping laws with fractional derivatives, Zeitschrift fur Angewandte Mathematic und Mechanic 75:623-635.MATHMathSciNetGoogle Scholar
  7. 7.
    Gaul L (1999) The influence of damping on waves and vibrations, Mech. Syst. Signal Process. 13:1-30.CrossRefGoogle Scholar
  8. 8.
    Catania G, Sorrentino S (2006) Fractional derivative linear models for describing the viscoelastic dynamic behaviour of polymeric beams, Saint Louis, Missouri, MO Proceedings of IMAC 2006.Google Scholar
  9. 9.
    Ewins DJ (2000) Modal Testing: Theory, Practice and Application, 2nd edition, Research Studies Press Baldock, UK.Google Scholar
  10. 10.
    Bagley RL, Torvik PJ (1983) Fractional calculus: a different approach to the analysis of viscoelastically damped structures, AIAA J. 21:741-748.MATHCrossRefGoogle Scholar
  11. 11.
    Sorrentino S (2003) Metodi analitici per lo studio di sistemi vibranti con operatori differenziali di ordine non intero, PhD thesis, Politecnico di Torino.Google Scholar
  12. 12.
    Sorrentino S, Garibaldi L (2004) Modal analysis of continuous systems with damping distributions defined according to fractional derivative models, Leuven (Belgium), Proceedings of Noise and Vibration Engineering Conference (ISMA 2004).Google Scholar
  13. 13.
    McCrum NG, Buckley CP, Bucknall CB (1988) Principles of Polymer Engineering, Oxford University Press, Oxford.Google Scholar
  14. 14.
    Miller KS, Ross B (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.MATHGoogle Scholar
  15. 15.
    Timoshenko S, Young DH (1955) Vibrations Problems in Engineering, 3rd edition, Van Nostrand New York.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Giuseppe Catania
    • 1
  • Silvio Sorrentino
    • 1
  1. 1.Department of MechanicsUniversity of BolognaItaly

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