Identification of fractional-derivative-model parameters of viscoelastic materials from measured FRFs

The dynamic properties of viscoelastic damping materials are highly frequency- and temperature-dependent. Numerical methods of structural and acoustic systems require the mathematical model for these dependencies. The fractional-derivative model on damping material has become a powerful solution that describes the frequency-dependent dynamic characteristics of damping materials. The model parameters on a damping material are very important information both for describing the responses of damped structures and in the design of damped structures. The authors proposed an efficient identification method of the material parameters using an optimization technique, showing its applicability through numerical studies in a previous work. In this study, the proposed procedure is applied to a damping material to identify the fractional-derivative-model parameters of viscoelastic materials. In the proposed method, frequency response functions (FRFs) are measured via a cantilever beam impact test. The FRFs on the points identical to those measured are calculated using an FE model with the equivalent stiffness approach. The differences between the measured and the calculated FRFs are minimized using a gradient-based optimization algorithm in order to estimate the true values of the parameters. The FRFs of a damped beam structure are measured in an environmental chamber at different temperatures and used as reference responses. A light impact hammer and a laser vibrometer are used to measure the reference responses. Both linear and nonlinear relationships between the logarithmically scaled shift factors and temperatures are examined during the identification of the material parameters. The applied results show that the proposed method accurately identifies the fractional-derivative-model parameters of a viscoelastic material. (C) 2009 Elsevier Ltd. All rights reserved.