報告題目：Application of Fractional Calculus for the Analysis of Nonlinear Damped Vibrations of Suspension Bridges

報告人：  Prof. Marina Shitikova （Voronezh State Technical University, Russia）

報告時間： 2019年10月31日（周四）上午 11:00

報告地點：明故宮校區(qū)A18-807

主辦單位：機械結構力學及控制國家重點實驗室、航空學院、科協(xié)、國際合作處

報告內(nèi)容簡介：

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.

報告人簡介：

Marina Shitikova，俄羅斯沃羅涅日國立技術大學教授，美國機械工程師協(xié)會、美國聲學協(xié)會、歐洲機械協(xié)會成員，曾是德國DAAD 訪問研究員，并獲得過美國Fulbright Senior Fellowship。她的研究小組（Center on Fundamental Research in Dynamics of Solids and Structures）在結構振動的建模和實驗研究方面很有建樹，特別是在分數(shù)階導數(shù)阻尼建模和非線性振動理論方面頗具實力。Shitikova教授有20多年的科研工作經(jīng)驗，多次到美國和德國參加學術交流；近年來主持了多個國際合作、俄羅斯國家科研基金以及新工程設計規(guī)范分析項目。她在工程力學頂級刊物ASME Applied Mechanics Review上發(fā)表過多篇論文，文章引用率高，其學術成果得到國際同行的廣泛認可。