New Methods for Identifying Rheological Parameter for Fractional Derivative Modeling of Viscoelastic Behavior
Tóm tắt
The modelling of viscoelastic behaviour by fractional derivatives, thegraphical method called the TIBI Diagram that is developed in this article, is anew approach, completely different from the classical methods, which aresomewhat inspired by the BODE diagram technique. The TIBI technique permits thereduction to a strict minimum of two break frequencies, which is theminimum number necessary, while the other graphical methods ofidentification require up to ten parameters to determine linear viscoelastic behaviour.The second method developed in this paper is a numerical approachwhich is very flexible with regard to the experimental complex moduluspermitting the determination of rheological characteristics. One needs a group offrequencies limited only to the transition region of the material.These two original methods are combined in certain cases to obtainsemi-graphical techniques.Experimental and simulation results are presented for each methodwith comparative analysis.
Tài liệu tham khảo
Bagley, R.L., ‘A theoretical basis of the application of fractional calculus to viscoelasticity’, J. Rheol. 27(3), 1983, 201–210.
Bagley, R.L. and Torvik, P.J., ‘Fractional calculus — A different approch to the analysis of viscoelastic damped structures’, AIAA J. 21(5), 1983, 741–748.
Bagley, R.L. and Torvik, P.J., ‘Fractional calculus in the transient analysis of viscoelastically damped structures’, AIAA J. 23(6), 1985, 918–925.
Bagley, R.L. and Torvik, P.J., ‘On the fractional calculus model of viscoelastic behavior’, J. Rheol. 30(1), 1986, 133–155.
Beda, T. and Vinh, T., ‘Technique d'identification des paramètres rhéologiques du modèle à dérivées fractionnaires des matériaux viscoélastique (Identification technique of rheological parameters of viscoelastic materials)’, Mécanique Matériaux Electricité 441, 1991, 1–6 [in French].
Beda, T., ‘Modules complexes des matériaux Viscoélastiques par essais dynamiques sur tiges — Petites et grandes déformations (Dynamic testing of complex moduli of viscoelastic beams — Small and large strains)’, Ph.D. Thesis, CNAM, Paris, 1990 [in French].
Koeller, R.C., ‘Application of fractional calculus to the theory of viscoelasticity’, J. Appl. Mech. 51, 1984, 299–307.
Nashif, A.H., Jones, D.I.G. and Henderson, J.P., Vibration Damping, John Wiley, New York, 1975.
Rogers, L., ‘Operators and fractional derivates for viscoelastic constitutive equations’, J. Rheol. 27(4), 1983, 351–372.
Rogers, L., ‘A new algorithm for interconversion of the mechanical properties of viscoelastic materials’, in Proceedings of the AIAA Dynamic Specialists Conference, Palm Springs, CA, May 17–18, 1984, Paper No. 84–1038 CP.
Rogers, L., ‘An accurate temperature shift function and a new approach to modeling complex modulus’, in Proceedings of the 60th Shock and Vibration Symposium, Cavalier Hotel, Virginia Beach, VA, 14–16 November, 1989, 1–19.
Soula, M., Vinh, T. and Chevalier, Y., ‘Transient responses of polymers and elastomers deduced from harmonic responses’, J. Sound Vibration 205(2), 1997, 185–203.