报告题目： Fractional derivatives in viscoelastic models and their organic relation with Rabotnov’s fractional exponential operator
报 告 人：Marina Shitikova教授，俄罗斯沃罗涅日国立建筑大学
时 间：2015年11月20日（周五）上午09:00-11:00
地 点：江宁校区乐学楼（1116室）
报告摘要：
Fractional derivatives in viscoelastic models and their organic relation with Rabotnov’s fractional exponential operator
The simplest viscoelastic models involving fractional derivatives, namely: fractional derivative Kelvin-Voigt model, Maxwell model, standard linear solid model and Koeller model, which are the generalization of the fractional derivative standard linear solid model, are reviewed, and their connectedness with the Rabotnov dimensional fractional operators is revealed. Using the resolvent operators for each model, which allow one to express not only the stress in terms of the strain but the strain in terms of the stress as well, it has been shown that not all of the simplest fractional derivative models retain their physical meaning when the fractional parameter vanishes to zero.
The role of the resolvent operators is shown for each of the models under consideration, since they allow one to define the physical meaning of the parameters involving in these models. For the Koeller model, it is demonstrated its connectedness with the generalized Rabotnov model involving the sum of Rabotnov fractional operators under the certain restrictions for the coefficients entering into the Koeller model. For the generalized Rabotnov models, formulas coupling the relaxation and retardation times with the elastic moduli entering in these models have been deduced.
In conclusion it is emphasized that nowadays the ideas of the Russian Academician Rabotnov are still widely used worldwide for solving intricate static and dynamic problems dealing with behavior of hereditarily elastic bodies.
报告人简介：
Marina Shitikova，俄罗斯沃罗涅日国立建筑大学教授，美国机械工程师协会、美国声学协会、欧洲机械协会成员，曾是德国DAAD 访问研究员，并获得过美国Fulbright Senior Fellowship。她的研究小组（Center on Fundamental Research in Dynamics of Solids and Structures）在结构振动的建模和实验研究方面很有建树，特别是在分数阶导数阻尼建模和非线性振动理论方面颇具实力。
Shitikova教授有20多年的科研工作经验，多次到美国和德国参加学术交流；近年来主持了多个国际合作、俄罗斯国家科研基金以及新工程设计规范分析项目。她在工程力学顶级刊物ASME Applied Mechanics Review上发表过多篇论文，文章引用率高，其学术成果得到国际同行的广泛认可。
