Читать книгу Modern Trends in Structural and Solid Mechanics 2 - Группа авторов - Страница 24

Professor Elishakoff enjoys historiography of science and his historical research is read with great interest. Bubnov or Galerkin? Timoshenko or Ehrenfest? The chicken or the egg?

We also provided a little historical research. Bolotin wrote about the possibility of extending the range of applicability of DEEM to PDEs with variable coefficients (Bolotin et al. 1961, Chapter II): “If the coefficients of the equation change slowly, then it is advisable to combine this method with the Wentzel–Brillouin–Kramers method or its related Blumenthal-Shtaerman approach” (translated by us). After reading the relevant papers, we were convinced that Blumenthal used the “WKB method”, created to solve problems of quantum mechanics in 1926, already in 1912 (Blumenthal 1912, 1914). He created this asymptotic method for solving problems of the shell theory. H. Reissner used Blumenthal’s approach in 1912 (Reissner 1912), as did Shtaerman in 1924 (Shtaerman 1924).

With these remarks, we are certainly not going to interfere with the complex priority history of the WKB approach (Wikipedia 2020). We recall Nayfeh’s remark concerning one well-known asymptotic method (Nayfeh 2000, p. 232): “The method of multiple scales is so popular that it is being rediscovered just about every 6 months”. A lot of phenomena in completely different fields of science are described using similar or directly identical equations. Researchers, as a rule, do not search for methods of their solution in areas far from them, but simply rediscover them. The corresponding methods are naturally given different names in different fields of science. Surprisingly, this does not lead to the “Tower of Babel effect”.