Robust identification of the mechanical properties of viscoelastic non standard materials by means of frequency domain experimental measurements

This work presents an identification procedure for the constitutive model of viscoelastic non-standard materials, such as Functionally Graded Materials (FGM). A generalized Kelvin model of arbitrary order is selected, making it possible to define the material constitutive relationship by means of the ratio of polynomials in the frequency domain. Since ill-conditioning may occur at the numerical identification stage of high order model parameters, a novel approach to identify the model optimal order and parameters, mainly employing a orthogonal polynomial basis, is proposed in this paper. Least square error fitting techniques employing a classic monomial and a Forsythe orthogonal polynomial basis are compared by starting from numerically estimated measurements with noise. The selected approach is used to fit dynamical measurement data obtained from real test specimens in a wide excitation frequency range. The optimal model results obtained by fitting real experimental data are presented and discussed.