Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions |
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Authors: | Xu Mingyu Tan Wenchang |
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Institution: | 1. Institute of Mathematics and Systematical Science, Research Center for Biomedical Engineering, Shandong University, Jinan 250100, China 2. Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China |
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Abstract: | The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a "compatibility equation" is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper. |
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Keywords: | viscoelastic material constitutive equation generalized fractional element networks fractional calculus generalized solution |
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