AN ALGEBRAIC NON-PARAMETRIC TECHNIQUE FOR THE IDENTIFICATION OF A FRACTIONAL MATERIAL MODEL

The identification of a fractional SLS model from E(jω) complex modulus experimental estimates is a challenging task and many approaches based on optimization techniques and assuming a N model order are known, nevertheless they strongly depend on the initial choice of the unknown model parameters. A fractional SLS model can be expressed as a rational polynomial formulation by means of a change of the jω variable and a parametric material model identification procedure based on the approach proposed by Levy, assuming the numerator and denominator polynomial orders are known in advance, was proposed in the past by some researchers in this field. A non-parametric procedure is here proposed, making it possible to identify a fractional SLS material model from E-^1(jω) discrete experimental estimate, where N is assumed to be not known in advance, and no a priori assumption is made on the derivative order of the dissipative material model components. E^-1(jω) estimate is typically obtained by means of forced excitation vibrational measurements at fixed frequency values, however such experimental tests are limited in the lower frequency range by experimental time constraints because the lower the frequency the higher the testing time is required. Nevertheless, the relaxation behavior of some high damping nonstandard materials is typically dependent on E^-1(jω) at low frequency values. E^-1(jω) can be experimentally estimated by processing quasi static relaxation measurements in the time domain. In this work J(t) creep compliance measurements are experimentally obtained and directly converted to E^-1(jω) estimate by using a known algorithm customized for the materials herein considered. In this work the inverse complex modulus estimate at low frequency (f < 0.1 Hz) obtained from this approach are used with the inverse complex modulus estimate at higher frequency (f > 0.1 Hz) obtained from forced excitation vibrational measurements, in order to take into account of a wide frequency range, so that the identified models can accurately simulate both quasi static and high frequency dynamic behavior, increasing the accuracy and the engineering application range of the identified material model.