New Methods for Identifying Rheological Parameter for Fractional Derivative Modeling of Viscoelastic Behavior

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.