Analysis of four-parameter fractional derivative model of real solid materials. (English) Zbl 1235.34026

Pritz, T.

J. Sound Vib. 195, No. 1, 103-115 (1996).

Summary: The introduction of fractional derivatives into the constitutive equation of the differential operator type of linear solid materials has led to the development of the so-called fractional derivative models. One of these models, characterized by four parameters, has been found usable for describing the variation of dynamics elastic and damping properties in a wide frequency range, provided that there is only one loss peak. In this paper this four-parameter model is theoretically analyzed. The effect of the parameters on the frequency curves is demonstrated, and it is shown that there is a strict relation between the dispersion of the dynamic modulus, the loss peak and the slope of the frequency curves. The half-value bandwidth of the loss modulus frequency curve is investigated, and conditions are developed to establish the applicability of the model for a class of materials. Moreover, it is shown that the model can be used to predict the frequency dependences of dynamic properties for a wide range even if measurements are made in only a narrow frequency range around the loss peak.

MSC:

34A08

Fractional ordinary differential equations