Statistical origins of fractional derivatives in viscoelasticity

Journal of Sound and Vibration

Volumn 284, Issue 3-5, 2005, Pages 1239-1245

  Chatterjee, Anindya ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; DAMPING; INVARIANCE; STATISTICAL METHODS; STRETCHING; STRUCTURAL DESIGN;

EXPONENTIAL DECAY; FRACTIONAL DERIVATIVES; INVARIANT SYSTEMS; NONINFINITESIMIAL MEMORY;

VISCOELASTICITY;

EID: 18444384521     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsv.2004.09.019     Document Type: Article

References (15)

1. D.L. Huber Statistical model for stretched exponential relaxation in macroscopic systems Physical Review B 31 9 1985 6070 6071
2. M.O. Vlad, B. Schönfisch, and M.C. Mackey Fluctuation-dissipation relations and universal behavior for relaxation processes in systems with static disorder and in the theory of mortality Physical Review E 53 5 1996 4703 4710
3. M.O. Vlad, R. Metzler, and J. Ross Generalized Huber kinetics for nonlinear rate processes in disordered systems nonlinear analogs of stretched exponential Physical Review E 57 6 1998 6497 6505
4. R.L. Bagley, and P.J. Torvik A theoretical basis for the application of fractional calculus to viscoelasticity Journal of Rheology 27 3 1983 201 210
5. R.L. Bagley, and P.J. Torvik On the fractional calculus model of viscoelastic behavior Journal of Rheology 30 1 1986 133 155
6. C.G. Koh, and J.M. Kelly Application of fractional derivatives to seismic analysis of base isolated models Earthquake Engineering and Structural Dynamics 19 1990 229 241
7. Y.A. Rossikhin, and M.V. Shitikova Application of fractional calculus for analysis of nonlinear damped vibrations of suspension bridges Journal of Engineering Mechanics 1998 1029 1036
8. M. Enelund, and G.A. Lesieutre Time domain modeling of damping using anelastic displacement fields and fractional calculus International Journal of Solids and Structures 36 1999 4447 4472
9. T.M. Atanakovic, and B. Stankovic Dynamics of a viscoelastic rod of fractional derivative type Zeitschrift für Angewandte Mathematik und Mechanik 82 6 2002 377 386
10. T.M. Atanakovic A modified Zener model of a viscoelastic body Continuum Mechanics and Thermodynamics 14 2002 137 148
11. K.B. Oldham, and J. Spanier The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order 1974 Academic Press New York
12. B.A. Finlayson The Method of Weighted Residuals and Variational Principles 1972 Academic Press New York
13. M. Enelund, L. Mähler, K. Runesson, and B.L. Josefson Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws International Journal of Solids and Structures 36 1999 2417 2442
14. A. Lion On the thermodynamics of fractional damping elements Continuum Mechanics and Thermodynamics 9 1997 83 96
15. A. Lion A physically based method to represent the thermo-mechanical behaviour of elastomers Acta Mechanica 123 1997 1 25