Distribution of Relaxation Times in Viscoelastic Inhomogeneous Media

• Autorzy: Soczkiewicz M.
• Języki publikacji: EN

Abstrakty

EN

Applying Ter Haar, Alfrey, and Gross approximations, we have calculate distributions of viscoelastic relaxation times for relaxation functions given by Schiessel et al. Fractional derivatives calculus has been applied to Maxwell model of viscoelasticity and it has been proved by means of the Gross formula that fractional derivatives brought about appearance od continous spectrum of viscoelastic relaxation frequencies. The width of this spectrum depends on the value of the fractional parameter alfa.

Słowa kluczowe

EN

viscoelasticity; relaxation times; fractional calculus

• Wydawca: Silesian Division of Polish Acoustical Society
• Czasopismo: Molecular and Quantum Acoustics
• Rocznik: 2003
• Tom: Vol. 24
• Strony: 161--168
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Soczkiewicz M.

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

Bibliografia

• 1. E. Soczkiewicz, 50 Otwarte Seminarium z Akustyki, Szczyrk-Gliwice, 22-27 Sept.2003, pp. 309-312.
• 2. H. Schiessel, R. Metzler, A. Blumen and T. Nonnenmacher, J. Phys. A: Math. Gen. 28, 6557-6584 (1995).
• 3. R. L. Bagley, J. Rheology 27(3), 201-210 (1983).
• 4. B. Gross, Mathematical Structure of the Theories of Viscoelasticity, Herman Editeurs, Paris 1953.
• 5. Y. A. Rossikhin and M. V. Shitikova, Mechanics of Time-Dependent Materials 5, (31- 175 (2001).
• 6. E. Soczkiewicz, Mol. Quant. Acoust. 23, 397-404 (2002).
• 7. S. G, Samko, A. A. Kilbas and O. I. Marichev, FractionalIntegrals and Derivatives, Gordon and Breach, Amsterdam 1993.
• 8. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York 1974.
• 9. K, S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Willey, New York 1997.
• 10. Y. A. Rossikhin and M. V. Shitikova, App. Mech. Rev. 50(1), 15-67 (1997).