报告题目：Asymptotics of ultrasonic sounding field in anisotropic materials

报告时间：2025年5月21日，星期三，下午14:00-15:00PM

报告地点：龙赛理科楼南楼 519会议室

主讲人：Prof. Evgeny Glushkov, Prof. Natalia Glushkova Kuban State University, Krasnodar, Russia

摘要：

To model the wave field of an ultrasonic transducer in materials with strong anisotropy (monocrystalline alloys of turbine blades, composite materials, welded joints, etc.), a physically descriptive asymptotic representation is obtained for quasi-spherical body waves excited by a surface source in an arbitrarily anisotropic elastic half-space. The asymptotics is derived by the stationary phase method from the integral representation of the solution in terms of contour integrals of the inverse Fourier transform. The peculiarities of their derivation and numerical implementation are discussed on the examples of a transversely isotropic composite material and a monocrystalline nickel alloy with cubic anisotropy. The dependence of the stationary points on the direction is more complicated here than in the isotropic case, up to the appearance of multiple stationary points and folds, giving rise to additional wave fronts and caustics. A comparison is made with the plane waves described by eigensolutions of the classical Christoffel equation. It is shown that, despite the phenomenon of multiple wave fronts, varying the plane-wave orientation allows us to obtain the same group velocity vectors as for any of the waves described by the asymptotics. The asymptotics is validated by numerical integration and illustrated with several numerical examples. In particular, in the present talk we discuss the influence of anisotropy on the source energy partition, radiation diagrams and wave energy fluxes, which are visualized by the time-averaged Umov-Poynting vectors and tangential to them energy streamlines.

主讲人简介：

Evgeny Glushkov is a Principal Investigator of the Institute for Mathematics, Mechanics and Informatics and Professor of the Department of Computer Technologies and Applied Mathematics, Kuban State University, Krasnodar, Russia. He received his PhD and DrSc degrees (Phys-Math) for the research in wave processes in solids and structures from the Rostov State University in 1978 and Leningrad State University in 1988, respectively; Laureate of the Russian State Prize for Science and Technology, 2002. Currently, his research interests focus on resonance wave phenomena, restoration of material properties from wave probing data, and wave dynamics of piezoelectric smart structures. He has published over 50 peer-reviewed journal articles (Ultrasonics, JASA, Smart Materials and Structures, Sound and Vibration, Wave Motion, etc.) and two monographs. 

Natalia Glushkova is a Principal Investigator of the Institute for Mathematics, Mechanics and Informatics and Professor of the Department of Computer Technologies and Applied Mathematics, Kuban State University, Krasnodar, Russia. She received her PhD and DrSc degrees (Phys-Math) for the research in wave processes in solids and structures from the Rostov State University in 1982 and 2000, respectively. Currently, her research interests focus on resonance wave phenomena and piezoelectric smart structures. She has published over 50 peer-reviewed journal articles (Ultrasonics, JASA, Smart Materials and Structures, Sound and Vibration, Wave Motion, etc.) and the monograph Integral Transforms and Wave Processes.