Frequency domain identification of the fractional Kelvin-Voigt's parameters for viscoelastic materials

In this work, a new innovative method is used to identify the parameters of fractional Kelvin-Voigt constitutive equation. These parameters are: the order of fractional derivation operator, 0 <= alpha <= 1, the coefficient of fractional derivation operator, C-V, and the stiffness of the model, K-V. A particular dynamic test setup is developed to capture the experimental data. Its outputs are time histories of the excitation and excited accelerations. The investigated specimen is a polymeric cubic silicone gel material known as alpha-gel. Two kinds of experimental excitations are used as random frequencies and constant frequency harmonic excitations. In this study, experimental frequency response functions confirm that increasing the static preload changes the behavior of the investigated viscoelastic material and the fractional Kelvin-Voigt model loses its validity by increasing the precompression. It is shown that, for a random frequencies excitation, by transforming from the time domain to the frequency domain the mentioned parameters can be identified. Using the identified parameters, analytical frequency response functions are so close to their experimental counterparts. Also, analytically produced time histories of the test setup's output for steady-state experimental tests are so close to the captured time histories. The mentioned results validate the procedure of identification.