We present a new approach to determine the rheological parameters of a mechanical model of viscoelastic materials. The fractional derivative solid model composed of a spring in series with a fractional derivative Kelvin–Voigt element has been employed to characterize the dynamic mechanical response of a real viscoelastic material. In dynamic mechanical analysis (DMA) measurements, the frequency-dependent loss modulus is plotted against the storage modulus in the form of complex plane plot. We find that the complex plane plot of the fractional derivative solid model is a depressed or distorted semicircle with its center below the real axis. The model parameters could be identified graphically via its complex plane curve, from which the spring constants can be obtained through the two intercepts of the extrapolated circular arc with the real axis, whereas the order of fractional dashpot can be estimated by the displacement of the semicircle center. The graphical method allows us to easily find rheological parameters, without using complicated calculation and special algorithms.

我们提出了一种确定粘弹性材料力学模型流变参数的新方法。由弹簧与分数导数开尔文-沃格特元素串联组成的分数导数实体模型已被用来表征真实粘弹性材料的动态力学响应。在动态力学分析（DMA）测量中，频率相关的损耗模量相对于储能模量以复平面图的形式绘制。我们发现分数导数实体模型的复杂平面图是一个凹陷或扭曲的半圆，其中心在实轴以下。可以通过其复杂的平面曲线以图形方式识别模型参数，从中可以通过外推圆弧与实轴的两个截距从中获得弹簧常数，而分数减震器的阶数可以通过半圆中心的位移来估计。图形方法使我们能够轻松找到流变参数，而无需使用复杂的计算和特殊的算法。