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Katerina D. Papoulia Vassilis P. Panoskaltsis Nishu V. Kurup Igor Korovajchuk 《Rheologica Acta》2010,49(4):381-400
We develop rheological representations, i.e., discrete spectrum models, for the fractional derivative viscoelastic element
(fractional dashpot or springpot). Our representations are generalized Maxwell models or series of Kelvin-Voigt units, which,
however, maintain the number of parameters of the corresponding fractional order model. Accordingly, the number of parameters
of the rheological representation is independent of the number of rheological units. We prove that the representations converge
to the corresponding fractional model in the limit as the number of units tends to infinity. The representations extend to
compound fractional derivative models such as the fractional Maxwell model, fractional Kelvin-Voigt model, and fractional
standard linear solid. Computational experiments show that the rheological representations are accurate approximations of
the fractional order models even for a small number of units. 相似文献
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