報告題目：Classification of the Transient Waves in Cosserat-type Shell Structures

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

報告時間：2019年10月23日（周三）下午 16:00

報告地點：明故宮校區(qū)A18-807

主辦單位：航空學(xué)院、機(jī)械結(jié)構(gòu)力學(xué)及控制國家重點實驗室、國際合作處

報告簡介：

In the present paper, the method of ray expansions is developed for solving boundary-value dynamic problems dealing with the propagation of surfaces of strong discontinuity (wave surface-strip) in thin linearly elastic shells with Cosserat-type micro-structure. The equations of the three-dimensional theory of asymmetric elasticity are utilized, which are written in the ray coordinates in the vicinity of the wave surface by means of the theory of discontinuities and then are integrated over the coordinate perpendicular to the median surface of a thin body. It is assumed that the wave surface-strip remains perpendicular to the median surface of the shell all the time during its propagation; the discontinuities in the normal stresses in the direction of the normal to the middle surface can be ignored as compared to the discontinuities in stresses in the elastic shell’s middle surface itself and in the layers parallel to it. These assumptions lead to the generation of four wave surfaces propagating in the shell with Cosserat-type micro-structure with the velocities of longitudinal and transverse waves obeying Kirchoff-Love hypothesis, as well as rotational and flexural waves due to microstructure of elastic thin bodies. As this takes place, on the longitudinal wave, the bulk deformations experience a discontinuity not only at the sacrifice of shortening-elongation of the medium’s element locating in the shell’s middle surface aligned perpendicular to the wave surface-strip, but also at the expense of thickening-thinning of this element in the direction perpendicular to the median surface of the body. On the transverse wave, there exist discontinuities in the components of the velocities directed along the middle surface and transversely to it.

The advantage of the developed approach lies in the fact that the found wave velocities depend only on material constants and are independent of any additional coefficients involving the geometry of thin bodies. The classification of the transient waves has been provides, which is necessary for further solution of different of boundary-value problems by the ray method, when the values to be found are represented in terms of the power series, the coefficients of which are the discontinuities in arbitrary order partial time-derivatives of the desired functions, while the time of arrival of the wave front is the independent variable..

報告人簡介：

Marina Shitikova，俄羅斯沃羅涅日國立技術(shù)大學(xué)教授，美國機(jī)械工程師協(xié)會、美國聲學(xué)協(xié)會、歐洲機(jī)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(jié)構(gòu)振動的建模和實驗研究方面很有建樹，特別是在分?jǐn)?shù)階導(dǎo)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(xué)術(shù)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(shè)計規(guī)范分析項目。她在工程力學(xué)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(xué)術(shù)成果得到國際同行的廣泛認(rèn)可。