黏弹性材料复模量和复柔量的分数阶微积分表述  

Expressions of fractional calculus for the complex modulus and complex compliance of viscoelastic materials

作　　者：金辉[1] 苏海军[1] 

机构地区：[1]山东大学数学与系统科学学院,山东济南250100

出　　处：《山东大学学报（理学版）》2005年第4期1-6,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10426024;10272067;10426023);教育部博士点专项科研基金资助项目(20030422046)

摘　　要：在分数阶微积分的理论框架下,将分形动力学的机制引入到生物黏弹性本构方程的研究中.应用广义分数阶单元网络方法,取消Schiessel等人对分数阶单元网络所做的参数限制,考察了黏弹性体的复模量、复柔量问题,将模型解的构造扩充至广义函数空间,从而给出更多具有明显物理意义的解.Within the framework of the fractional calculus theory, the mechanism of fractal dynamics is introduced to the constitutive equation research of viscoelastic materials. The restriction of all parameters in fractional element advanced by Schiessel et al is cancelled by using generalized fractional element technique. The complex modulus and complex compliance of viscoelastic materials are studied. The solutions are extended to generalized function space, and more solutions with distinct physical meaning are obtained.

关 键 词：黏弹性材料 复模量 复柔量 分数阶微积分 

分 类 号：O035[理学]