Fractional derivative linear models for describing the viscoelastic dynamic behaviour of polymeric beams

Non integer, fractional derivative order rheological models are known to be very effective in describing the linear viscoelastic dynamic behavior of mechanical structures made of polymers. The application of fractional calculus to viscoelasticity can be physically consistent and the resulting non integer order differential stress-strain constitutive relation provides good curve fitting properties, requires only a few parameters and leads to causal behavior. In this paper a fractional Zener model is adopted for describing the viscoelastic dynamic behavior of High Density Polyethylene (HDPE) beams. A procedure for estimating an equivalent damping ratio is introduced, in order to check the ability of the selected model in reproducing experimentally obtained damping estimates. A frequency domain technique is then proposed to compute the frequency dependent complex stress-strain relationship parameters related to the material.