Non-conventional rheological models based on non-integer order differential operators can be used to describe the viscoelastic behavior of materials, especially of polymers. These models are usually selected and then validated by means of creep and relaxation tests. However, engineers dealing with structural dynamic problems may need to obtain model identification from vibration measurement data. In this case, however, the direct identification of an optimal set of parameters of a viscoelastic model from time or frequency domain measurements is a difficult task, especially if the structural dissipative contributions are slight. In this paper, an indirect approach is adopted, based on the concept of damping ratio. When dealing with standard linear viscous dissipative models, a damping ratio modal parameter ζn can be analytically defined and experimentally estimated. But this theoretical parameter shows a dependency from the modal frequency that may dramatically fail in fitting the experimental data. On the contrary, it is known that a better agreement between theory and experiments can be achieved by means of non-integer order differential models, even though in this case analytical expressions for ζn are difficult to find. To overcome this difficulty, a method of general validity for viscoelastic models is developed, based on the concept of equivalent damping ratio and on the circle-fit technique. The proposed method is applied to experimental damping estimates from plane flexural vibrations of clamped-free beams, obtained from specimens of different size made of materials such as Polyethylene, Polyvinyl-chloride and Delrin.

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