Identifying Fractional Viscoelastic Models Based on Surface Wave Motion

In previous studies of the second author mechanical wave motion on a viscoelastic material representative of biological tissue was analyzed. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and subsurface sources were considered. It was shown that a fractional order Voigt model, in which the damping component, dependent on the first derivative of time, is replaced with a fractional element dependent on a derivative of time of fractional order between 0 and 1, resulted in closer agreement with experiment as compared with the conventional (integer order) models of Voigt and Zener. In the present study different materials and a wider range of viscoelastic models are considered. An algorithm to evaluate the frequency-dependent shear moduli of viscoelastic materials measuring the propagation of Rayleigh waves on the surface of the media is presented and viscoelastic models (both of integer and fractional order) are compared to experimental results. It is shown that, in the frequency range of interest (100–600 Hz), the use of the fractional order assumption improves the match of theory to experiment.