报告题目：Application of Fractional Calculus for the Analysis of Nonlinear Damped Vibrations of Suspension Bridges
报告人： Prof. Marina Shitikova （Voronezh State Technical University, Russia）
报告时间： 2019年10月31日（周四）上午 11:00
报告地点：明故宫校区A18-807
主办单位：机械结构力学及控制国家重点实验室、航空学院、科协、国际合作处
报告内容简介：
This lecture is devoted to the analysis of dynamic behavior of suspension bridges subjected to the different conditions of the internal resonances.
First we consider nonlinear free damped vibrations of a suspension bridge with a bisymmetric stiffening girder under the conditions of the internal resonance one-to-one, i.e., when natural frequencies of two dominating modes - a certain mode of vertical vibrations and a certain mode of torsional vibrations - are approximately equal to each other, or two-to-one, when one frequency is twice larger than the other. Damping features of the system are defined by fractional derivatives with fractional parameters (the orders of the fractional derivatives) changing from zero to one. It is assumed that the amplitudes of vibrations are small but finite values, and the generalized method of multiple scales suggested in is used as a method of solution. The influence of uncertainty in choosing the fractional parameters on the character of nonlinear damped vibrations of suspension bridges is investigated.
Then nonlinear forced vibrations of suspension bridges, when the frequency of an external force is approaching one of the natural frequencies of the suspension system, which, in its turn, undergoes the conditions of the one-to-one internal resonance, are investigated via the generalized method of multiple time scales. The damping features are described by the fractional derivative, which is interpreted as the fractional power of the differentiation operator. The influence of the fractional parameters (orders of fractional derivatives) on the motion of the suspension bridge model is investigated.
报告人简介：
Marina Shitikova，俄罗斯沃罗涅日国立技术大学教授，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。
