Читать книгу Modern Trends in Structural and Solid Mechanics 2 - Группа авторов - Страница 15

Professor Isaac E. Elishakoff was a doctoral student of the world-renowned scientist V.V. Bolotin (March 29, 1926 to May 28, 2008) (Bolotin 2006). The first research works of I. Elishakoff and his PhD thesis were devoted to the application and development of the dynamic edge effect (EE) method proposed by V.V. Bolotin. After moving from the Soviet Union to the Western world, Prof. Elishakoff made great efforts to popularize the dynamic EE method in the Western scientific community (Elishakoff 1974, 1976; Elishakoff and Wiener 1976).

Therefore, the appearance of a review of papers related to Bolotin’s method in the volume devoted to Prof. Elishakoff’s 75th birthday seems quite reasonable. Moreover, the previous comprehensive reviews of the subject were published in 1976 (Elishakoff 1976) and 1984 (Bolotin 1984).

In the early 1960s, V.V. Bolotin put forward an asymptotic method for studying natural oscillations of plates and shells, which used the inverse of the dimensionless vibration frequency as a small parameter (Bolotin 1960a, 1960b). In a more general formulation, it is a method for solving self-adjoint eigenvalue problems defined in a rectangular domain, called the boundary value problems with quasi-separable variables, according to Bolotin’s terminology. For this reason, the method is referred to as Bolotin’s method or the dynamic edge effect method (DEEM). And despite the fact that 60 years have passed since the method creation, it is still relevant. The purpose of this review is describing various generalizations and modifications of DEEM, the problems solved with the use of this method and also trying to determine the place of DEEM among the known methods for finding rapidly oscillating solutions. Thus, we demonstrate that DEEM can be broadly applied for solving modern problems.