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J4 ›› 2013, Vol. 48 ›› Issue (2): 88-92.

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利用分数阶导数模型研究有记忆的固体材料

黎明,徐明瑜   

  1. 山东大学数学学院, 山东 济南 250100
  • 收稿日期:2012-03-22 出版日期:2013-02-20 发布日期:2013-03-04
  • 作者简介:黎明(1968- ), 男,讲师,博士研究生,研究方向为分数阶微积分及其应用. Email: liming68@sdu.edu.cn
  • 基金资助:

    国家自然科学基金资助项目(10272067)

Toward a model for solid materials with memory by use of  the fractionalorder derivatives

LI Ming, XU Ming-yu   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2012-03-22 Online:2013-02-20 Published:2013-03-04

摘要:

 对一类带有不同分数阶导数的黏弹性材料本构方程进行了讨论,其解通过拉普拉斯变换得到,可用H-Fox函数表示,且解与实验数据拟合较好。在频率域模型的行为方面,损耗角正切的极限由应变和应力时间导数阶的差决定。

关键词: 分数阶导数;黏弹性;H-Fox函数

Abstract:

A constitutive equation on viscoelastic materials with different fractional order derivatives is discussed, and its solution is obtained by using Laplace transform techniques and can be expressed in terms of H-Fox functions.The solution is consistent with the experimental data.The model behavior in the frequency domain is also discussed, the limit of the loss tangent is governed by the difference between the order of time derivatives of strain and stress.

Key words:  fractional derivative;viscoelasticity; H-Fox function

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