A fractional derivative model with five parameters for rubber materials

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (23) : 37-41.

ZHAO Yong-ling1, HOU Zhi-chao1，HUANG You-jian2，LIU Jian-xun2

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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.

Key words

Cole-Cole curve / visco-elasticity / fractional derivative model / dynamic mechanics experiment / parameter identification

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ZHAO Yong-ling1, HOU Zhi-chao1，HUANG You-jian2，LIU Jian-xun2. A fractional derivative model with five parameters for rubber materials[J]. Journal of Vibration and Shock, 2015, 34(23): 37-41

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