A new identification method of viscoelastic behavior: Application to the generalized Maxwell model

Franck Renaud (1) , Jean-Luc Dion (1) , Gaël Chevallier (1) , Imad Tawfiq (1) , Rémi Lemaire (2)

1 LISMMA - Laboratoire d'Ingénierie des Systèmes Mécaniques et des MAtériaux
2 Bosch (Chassis System Brakes)

This paper focuses on the generalized Maxwell model (GMM) identification. The formulation of the transfer function of the GMM is defined, as well as its asymptotes. To compare identification methods of the parameters of the GMM, a test transfer function and two quality indicators are defined. Then, three graphical methods are described, the enclosing curve method, the CRONE method and an original one. But the results of graphical methods are not good enough. Thus, two optimization recursive processes are described to improve the results of graphical methods. The first one is based on an unconstrained non-linear optimization algorithm and the second one is original and allows constraining identified parameters. This new process uses the asymptotes of the modulus and the phase of the transfer function of the GMM. The result of the graphical method optimized with the new process is very accurate and fast.

Mots clés: Viscoelasticity; Identification; Generalized Maxwell; Fractional derivatives; Transfer function; Pole-zero

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

Franck Renaud, Jean-Luc Dion, Gaël Chevallier, Imad Tawfiq, Rémi Lemaire. A new identification method of viscoelastic behavior: Application to the generalized Maxwell model. Mechanical Systems and Signal Processing, 2011, 25, pp.991-1010. ⟨10.1016/J.YMSSP.2010.09.002⟩. ⟨hal-00708819⟩