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

International Conference on Manufacturing Technology, Materials and Chemical Engineering

材料科学;化学工业

Yin, Y.L.^1^2 ; Yang, Z.H.^1^2 ; Shi, M.L.^2

Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, 4800 Cao'an Road, Shanghai

201804, China^1

School of Materials Science and Engineering, Tongji University, 4800 Cao'an Road, Shanghai

201804, China^2

关键词: Dynamic mechanical analysis (DMA);    Dynamic mechanical test;    Fractional derivative model;    Fractional derivatives;    Parameter determination;    Sinusoidal perturbations;    Storage and loss modulus;    Visco-elastic material;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/592/1/012009/pdf
DOI  :  10.1088/1757-899X/592/1/012009

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

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.