Identification of Viscoelastic Materials

Abstract

The frequency-dependent complex modulus for a linearly viscoelastic material is estimated from wave propagation experiments. In these experiments, strains at different sections of a bar specimen are measured as functions of time. The time series are then transformed into the frequency domain, where the identification is made. Two identification techniques, a non-parametric and a parametric, are considered in the paper. Analyses of the quality of the estimates given by the two different techniques are carried out, and approximate expressions for the covariance matrices of the complex modulus are provided. The validity of these expressions are confirmed by numerical studies as well as by real experiments. A comparison between the results of the non-parametric and parametric approaches is made. The results of the comparison are that the parametric model describes the complex modulus quite well and that the variances for the parametric estimates are considerably smaller.