通过在分数导数Zener模型中增加Scott-Blair粘壶，建立了一种新的五参数分数导数模型。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。
Abstract
A fractional derivative model of five parameters is constructed by adding a Scott-Blair pot to the fractional derivative Zener model. Numerical analysis is conducted to understand the influence on the Cole-Cole curve of model parameters related to the fractional derivative operators. Dynamic mechanical analysis experiments are 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 are derived by taking advantage of the temperature equivalence principle, and model constants of the new fractional derivative model are identified. With validation from experiments, it is clearly demonstrated that the newly established fractional derivative model with five parameters can accurately describe the dynamic characteristics of rubber materials with a symmetric or asymmetric Cole-Cole curve.
关键词
Cole-Cole曲线 /
粘弹性 /
分数导数模型 /
动态力学实验 /
参数识别
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Key words
Cole-Cole curve /
visco-elasticity /
fractional derivative model /
dynamic mechanics experiment /
parameter identification
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参考文献
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