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. (C) 2016 Elsevier Ltd. All rights reserved.