Complex plane analysis of fractional derivative model and its use for parameter determination of viscoelastic material

Abstract

The mechanical properties of viscoelastic materials are usually described by a rheological model composed of spring and dashpot in series or in parallel or their combination. The complex modulus as a function of angular frequency was firstly deduced, when fractional derivative rheological model is subjected to a sinusoidal perturbation in dynamic mechanical analysis (DMA) measurements. Then, the algebraic equations between the storage and loss moduli of the fractional Zener model in complex plane have been developed. The curve on the complex plane, a plot of loss modulus against storage modulus, is a repressed or distorted semicircle with its center below the real axis. The parameters of mechanical elements can be graphically estimated from its complex plane plot. The dynamic mechanical test of bituminous mixtures was carried out by frequency sweep over a wide range of 200 Hz to 0.02 Hz and its mechanical response can be described adequately by the fractional Zener model, whose element parameters are determined via geometric method.