含分数阶导数的粘弹性固体模型及其应用  被引量：5

作　　者：刘朝辉 张为民[2] 

机构地区：[1]湖南轻工业高等专科学校,湖南长沙410015 [2]湘潭大学基础力学与材料工程研究所,湖南湘潭411105

出　　处：《株洲工学院学报》2002年第4期23-25,共3页Journal of Zhuzhou Institute of Technology

基　　金：湖南省教育厅重点资助项目 (99A0 1 );湖南省教育厅资助项目 (0 1C0 83)

摘　　要：从分数导数的定义出发 ,提出了在粘弹性经典模型理论中用Abel粘壶取代传统的牛顿粘壶的新观点 ,构造出来的含分数导数的标准线性体可以很好地描述真实材料的松弛和蠕变现象 ,并且其松弛模量和蠕变柔量可以严格作到Stieltjes卷积为单位阶跃函数 ;含分数导数的标准线性体模型可以在很宽广的频率范围内同时很好地模拟真实材料的存储模量和损耗模量 。The viscoelastic solid model with fractional order derivative is proposed in this paper. From the definition of fractional order derivative, the new idea that replaces the traditional Newton dashpot with Abel dashpot is also proposed . The standard linear body with fractional order derivative can successfully describe the relaxation and creep phenomenon of real material. The Stieltjes convolution of relaxation modulus and creep compliance is Heaviside unite step function strictly. The standard linear body with fractional order derivative can be satisfied with experiments of storage modulus and loss modulus of real material in very width frequency. It has extensive application foreground in the theory of viscoelastic.

关 键 词：粘弹性固体模型 分数阶导数 流变模型理论 本构方程 松驰模量 蠕变柔量 应用 定义 标准线性体模型 

分 类 号：O37[理学—流体力学] O172[理学—力学]