Analytical modelling and experimental identification of viscoelastic mechanical systems

In the present study non-integer order or fractional derivative rheological models are applied to the dynamical analysis of mechanical systems. Their effectiveness in fitting experimental data on wide intervals of frequency by means of a minimum number of parameters is first discussed in comparison with classical integer order derivative models. A technique for evaluating an equivalent damping ratio valid for fractional derivative models is introduced, making it possible to test their ability in reproducing experimentally obtained damping estimates. A numerical procedure for the experimental identification of the parameters of the Fractional Zener rheological model is then presented and applied to a high-density polyethylene (HDPE) beam in axial and flexural vibrations.