ANALYSIS OF FOUR-PARAMETER FRACTIONAL DERIVATIVE MODEL OF REAL SOLID MATERIALS

✍ Scribed by T. Pritz

• Book ID: 102608104
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 420 KB
• Volume: 195
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0406

✦ Synopsis

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.