The Comparison of Fractional Derivative Model and Classical Spring-Dashpot Model in the Identification of Viscoelastic Characteristics of a Rubber Material

Abstract

In the design of viscoelastic materials used in rubber products, not theoretical approaches but experimental approaches have been usually employed. This is due to the difficulties in mathematical procedures of the dynamic material characteristics such as the dependencies of strain amplitude, frequency and/or environmental temperature in deformation. In mathematical approach there are two kind of analytical models for a complex module of the material, which are a fractional derivative model and a spring-dashpot model. However there are few papers dealing with the study of the identifications of parameters for the experimental modulus actually obtained not only by using the fractional derivative model but also by using the spring-dashpot model and the discussion of the comparisons of the two models. In the present paper, the complex elastic modulus for a rubber material are obtained experimentally for a wide range of excitation frequency, and the modulus-frequency relations are derived analytically by using the two models, respectively. Finally, the applicability of the models are discussed from the numerical results.