Application of Fractional Calculus in the Theory of Viscoelasticity

• Autorzy: Soczkiewicz, E.
• Języki publikacji: EN

Abstrakty

EN

The fractional derivate method has been used in studies of the complex moduli and impedances for various models of viscoelastic substances. Calculations vave been performed for MAxwell and Barlow-Erginsav-Lamb models. Influence of the values of the fractional parameters on the frequency dependances of the complex moduli and impedances has been studied.

Słowa kluczowe

EN

viscoelasticity; fractional culculus

• Czasopismo: Molecular and Quantum Acoustics
• Rocznik: 2002
• Tom: Vol. 23
• Strony: 397-404
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Soczkiewicz, E.

• Institute of Physics, Silesian University of Technology Bolesława Krzywoustego 2, 44-100 Gliwice, Poland,

Bibliografia

• 1. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, Amsterdam 1993.
• 2. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York 1974.
• 3. K. S. Miller and B Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. Willey, New York 1993.
• 4. A. Carpinteri and F Mainardi, ed., Fractals and Fractional Calculus in Continum Mechanics,Springer, Wien,New York 1997.
• 5. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego 1999.
• 6. Y A. Rossikhin and M V Shitikova, Appl.Mech Rev. 50, 15-67 (1997).
• 7. Y. A. Rossikhin and M V Shitikova, 17th International Congress on Acoustics, Rome, September 2-7 (2001).
• 8. Y. A. Rossikhin and M. V. Shitikova, Mechanics of Time Dependent Materials 5, 131-175 (2001).
• 9. A. Carpinteri and P. Cometti, Chaos, Solitons and Fractals 13, 85-94 (2002).
• 10. Z. E. A. Fellah and C. Depollier, J. Sound and Vibration 244, 356-366 (2001).
• 11. F Mainardi, Chaos, Solitons and Fractals 7, 1461-1477 (1996).
• 12. T. Pritz, J. Sound and Vibration 195, 103-115 (1996).
• 13. P. J. Torvik and R. L. Bagley, Transactions ASME J. Appl. Mech. 51, 294-298 (1984).
• 14 R. C. Koeller, Transactions ASME J. Appl. Mech. 51, 299-307 (1984).
• 15 R L. Bagley, J. Rheology 27, 201-210(1983).
• 16. R Płowieć, Studies of Rheological Properties of Oils in the Range of Viscoelastic Relaxation, Reports of the Institute of Fundamental Technological Research, Warsaw 1975 (in Polish).
• 17. N. Makris and M. C. Costantinou, J. Structural Engineering ASCE 117(9). 2708- 2784 (1991).
• 18. Ch. Friedrich and H. Braun, Rheologica Acta 11(4), 309-322 (1992).
• 19. L. I. Palade, V. Vemey and P. Attane, Rheologica Acta 35(3), 265-273 (1996).
• 20. R. L. Bagley and P. J. Torvik, AIAA Journal 21(5), 741-748 (1983).
• 21. D R. Morgenthaler, Practical design and analysis of systems with fractional derivative materials and active control. Proceedings of Damping 91, San Diego 1991, vol. 1, p. BCA1-BCA28.
• 22. P. Cupial, Some approaches to the analysis of non-proportionally damped viscoelastic structures. Proceedings of the International Symposium on Dynamics of Continua, Bad Honnef, D. Besdo and R. Bogacz eds, Shaker Verlag 1996, p. 93- 102.
• 23. Ch. Friedrich, Relaxation functions of rheological constitutive equations with fractional derivatives: thermodynamic constraints.In: Rheological Modelling: Thermodynamical and Statistical Approaches, J. Casas-Vazques and D. Jou eds, Springer-Verlag, Berlin 1991, p 321-330.
• 24. G. Harrison, The Dynamic Properties of Supercooled Liquids, Academic Press, London 1976.