Unbounded complex modulus of viscoelastic materials and the Kramers-Kronig relations

Journal of Sound and Vibration

Volumn 279, Issue 3-5, 2005, Pages 687-697

  Pritz, T ^a  

^a Szikkti Labs   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; DISPERSION (WAVES); ELECTRODYNAMICS; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; NATURAL FREQUENCIES; REFRACTION;

COMPLEX MODULUS; DAMPING MATERIALS; FRACTIONAL DERIVATIVE; KELVIN MODEL;

VISCOELASTICITY;

EID: 9644303309     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsv.2003.11.040     Document Type: Article

References (28)

1. R. de L. Kronig, On the theory of the dispersion of X-rays, Journal of the Optical Society of America 12 (1926) 547-557.
2. H.A. Kramers, La diffusion de la lumiere par les atomes, Atti del Congresso Internazionale dei Fisici, Como 2 (1927) 545-557.
3. D.C. Champeney, Fourier Transforms and their Physical Applications, Academic Press, London, 1973.
4. B. Gross, Mathematical Structure of the Theories of Viscoelasticity, Hermann, Paris, 1953, p. 27.
5. T.D. Sermergor, On dispersion relations for elasticity and compliance, Prikladnaja Matematika i Tekhnicheskaia Fizika 1 (1960) 96-102 (in Russian).
6. M. O'Donnell, E.T. Jaynes, J.G. Miller, Kramers-Kronig relationship between ultrasonic attenuation and wave velocity, Journal of the Acoustical Society of America 69 (1981) 696-701.
7. H.C. Booij, G.P.J.M. Thoone, Generalization of Kramers-Kronig transforms and some approximations of relations between viscoelastic quantities, Rheologica Acta 21 (1982) 15-24.
8. N.W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behaviour: An Introduction, Springer, Berlin, 1989.
9. T. Pritz, Verification of local Kramers-Kronig relations for complex modulus by means of fractional derivative model, Journal of Sound and Vibration 228 (1999) 1145-1165.
10. L. Rogers, Operators and fractional derivatives for viscoelastic constitutive equations, Journal of Rheology 27 (1983) 351-372.
11. B.L. Fowler, Interactive characterization and data base storage of complex modulus data, Proceedings of Damping'89, Florida, Vol. 2, FAA 1-12, 1989.
12. C. Roland, C.A. Trask, Damping in polydienes, in: R.D. Corsaro, L.H. Sperling (Eds.), Sound and Vibration Damping with Polymers, ACS Symposium Series 424, American Chemical Society, Washington, DC, 1990, pp. 301-313.
13. D.I.G. Jones, Results of a Round Robin test program: complex modulus properties of a polymeric damping material, WL-TR-92-3104. Technical Report of Wright Laboratory, Ohio, 1992.
14. G.F. Lee, J.D. Lee, B. Hartmann, D. Rathnamma, Damping properties of PTMG/PPG blends, Proceedings of Damping '93, San Francisco, Vol.3, ICA 1-19, 1993.
15. C. Friedrich, H. Braun, Generalized Cole-Cole behaviour and its rheological relevance, Rheologica Acta 31 (1992) 309-322.
16. H. Schiessel, R. Metzler, A. Blumen, T.F. Nonnenmacher, Generalized viscoelastic models: their fractional equations with solutions, Journal of Physics A: Math-Gen. 28 (1995) 6567-6584.
17. L.I. Palade, V. Verney, P. Attané, A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime, Rheologica Acta 35 (1996) 265-273.
18. Y. A. Rossikhin, M.V. Shitikova, Analysis of rheological equations involving more than one fractional parameters by the use of the simplest mechanical systems based on these equations, Mechanics of Time-Dependent Materials 5 (2001) 131-175.
19. T. Pritz, Five-parameter fractional derivative model for polymeric damping materials, Journal of Sound and Vibration 265 (2003) 935-952.
20. J.D. Ferry, Viscoelastic Properties of Polymers, 2nd Edition, Wiley, New York, 1970.
21. B.E. Read, G.D. Dean, The Determination of Dynamic Properties of Polymers and Composites, Adam Hilger, Bristol, 1978, p. 183.
22. A.D. Nashif, D.I.G. Jones, J.P. Henderson, Vibration Damping, Wiley, New York, 1985.
23. R.M. Christensen, Theory of Viscoelasticity: An Introduction, Academic Press, New York, 1982.
24. M. Caputo, F. Mainardi, Linear models of dissipation in anelastic solids, Rivista del Nuovo Cimento 1 (1971) 161-198.
25. R.L. Bagley, P.J. Torvik, A generalized derivative model for an elastomer damper, Shock and Vibration Bulletin 49 (1979) 135-143.
26. R.L. Bagley, P.J. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, Journal of Rheology 27 (1983) 201-210.
27. C.G. Koh, J.M. Kelly, Application of fractional derivatives to seismic analysis of base-isolated models, Earthquake Engineering and Structural Dynamics 19 (1990) 229-241.
28. T. Pritz, Dynamic Properties of Materials for Vibration Control, Akadémiai Kiadó, 1996, pp. 116-117 (in Hungarian).