Transfer functions in the linear dynamic system theory are applied to characterize dynamic mechanical properties of viscoelastic materials. Correlation between transfer functions and typical rheological models and fractional derivative ones are briefly introduced. The transfer function of a rheological model may be expressed in terms of multiplication of factored polynomials. The frequency–response data are presented in the form of a Bode plot of magnitude, from which a transfer function can be established. The characteristic times can be conveniently identified via the corner frequencies of asymptotes of the magnitude curve. Dynamic frequency sweep results for a typical viscoelastic solid are presented to illustrate the use of the Bode diagram method for parameter identification.

中文翻译：

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粘弹性材料复模量的解析表达式

线性动态系统理论中的传递函数用于表征粘弹性材料的动态力学性能。简要介绍了传递函数与典型流变模型和分数导数模型的相关性。流变模型的传递函数可以用因式多项式相乘来表示。频率响应数据以幅度波特图的形式呈现，从中可以建立传递函数。通过幅度曲线的渐近线的拐角频率可以方便地识别特征时间。给出了典型粘弹性固体的动态频率扫描结果，以说明使用波特图方法进行参数识别。