报告题目：Classification of the Transient Waves in Cosserat-type Shell Structures

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

报告时间：2019年10月23日（周三）下午 16:00

报告地点：明故宫校区A18-807

主办单位：航空学院、机械结构力学及控制国家重点实验室、国际合作处

报告简介：

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..

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。