橡胶材料的一种5参数分数导数模型

A fractional derivative model with five parameters for rubber materials

通过在分数导数Zener模型中增加Scott-Blair黏壶,建立了一种新的5参数分数导数模型。分析了分数导数算子参数对Cole-Cole曲线形状的影响;基于某隔振橡胶材料的DMA实验,应用温—频等效原理获得了该材料的动态模量和损耗因子的主曲线,并识别了新建模型的全部参数。结果表明,该模型能够比较准确地反映具有对称或非对称Cole-Cole曲线的橡胶材料的动态特性。

A fractional derivative model with five parameters was constructed by adding a Scott-Blair pot to the fractional derivative Zener model. Numerical analysis was conducted to analyze the influence of parameters of the fractional derivative operators on Cole-Cole curves. Dynamic analysis tests were then performed on a rubber material usually used for vibration isolation. Using the measured data,the storage modulus,loss modulus and loss factor of the material were derived by adopting the temperature-frequency equivalence principle,and all parameters of the new fractional derivative model were identified. The results demonstrated that the newly established fractional derivative model with five parameters can accurately describe the dynamic characteristics of rubber materials with a symmetric or non-symmetric Cole-Cole curve.