Identification of non-conventional viscoelastic models for polymeric vibrating structures

In the field of structural vibrations, an appropriate rheological model should be accurate in fitting the experimental data on a wide interval of frequencies by means of a minimum number of parameters and, in particular, it should be able to reproduce the experimentally found behavior of the damping ratio ζn as a function of the natural angular frequency ωn. In this study a non-integer order differential linear rheological model is considered, and its effectiveness in solving the above mentioned problem is discussed. This model, refferred to as the Fractional Double Kelvin model, combines the properties of both the Fractional Kelvin and Fractional Zener models, which are considered to be very effective in describing the viscoelastic dynamic behavior of mechanical structures made of polymers. An identification method of general validity for viscoelastic models is adopted, based on the concept of equivalent damping ratio and on the circlefit technique. It is applied to the analysis of vibrating beams and plates of different sizes, made of polymeric materials such as Polyethylene, Polyvinyl-chloride and Delrin.