New methods for identifying rheological parameter for fractional derivative modeling of viscoelastic behavior

• Published in: Mechanics of time-dependent materials 2004-06, Vol.8 (2), p.105-118
• Main Authors: BEDA, T, CHEVALIER, Y
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 1385-2000; 1573-2738
• DOI: 10.1023/B:MTDM.0000027671.75739.10

The modelling of linear viscoelastic behavior using fractional derivatives is a principal theme in modern research into structural calculus. The interest in this approach lies in the fact that this mathematical model optimizes the number of rheological parameters that define viscoelastic behavior, unlike the classical integer order derivatives. The modelling of viscoelastic behaviour by fractional derivatives, the graphical method called the TIBI Diagram that is developed in this article, is a new approach, completely different from the classical methods, which are somewhat inspired by the BODE diagram technique. The TIBI technique permits the reduction to a strict minimum of two break frequencies, which is the minimum number necessary, while the other graphical methods of identification require up to ten parameters to determine linear viscoelastic behaviour. The second method developed in this paper is a numerical approach, which is very flexible with regard to the experimental complex modulus permitting the determination of rheological characteristics. One needs a group of frequencies limited only to the transition region of the material. These two original methods are combined in certain cases to obtain semi-graphical techniques. Experimental and simulation results are presented for each method with comparative analysis. (Example material: PIB.)