Propagation and Interaction of Weakly Nonlinear Elastic Waves in Anisotropic Materials


报告题目Propagation and Interaction of Weakly Nonlinear Elastic Waves in Anisotropic Materials

报告人  Prof. W?odzimierz DomańskiMilitary University of Technology



主办单位: 国际相助处、科协、机械结构力学及控制国家重点实验室、航空宇航学院


The importance of studying nonlinear mechanical waves is motivated in particular by the fact that such waves are excellent tools for analyzing different properties of materials like e.g. features of damage (cracks, flaws, etc.). Waves can distort in nonlinear materials and create higher harmonics. Unlike as it is in the linear case, the nonlinear waves may interact resonantly producing new waves which propagate with phases of frequencies being linear combination of the original ones. These phenomena are remarkably large in damaged materials in comparison to the undamaged ones. The sensitivity of nonlinear methods to the detection of damage features is much greater than that of linear acoustical methods.


Mathematical models of wave type phenomena in real media, typically lead to very complicated nonlinear systems of partial differential equations. This is particularly true when there are several fields involved in the modeling process. In such cases the governing set of equations is usually too complicated to deduce from it analytically any qualitative results about its solution. Therefore in order to describe a nonlinear wave motion in such complicated cases, one may attempt to derive simpler models of a real phenomenon.


The talk will present the method of weakly nonlinear multiple-scale asymptotics which provides simplified models for propagation and interaction of nonlinear waves. The talk will be illustrated by examples which emphasize differences in behavior of nonlinear longitudinal and shear waves in isotropic and anisotropic elastic materials.



W?odzimierz Domański, is currently a Professor of the Institute of Mathematics and Cryptology, a faculty of Cybernetics at the Military University of Technology. He was a Fulbright Postdoctoral Fellow Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, USA.