Modern Trends in Structural and Solid Mechanics 2. Группа авторов

Modern Trends in Structural and Solid Mechanics 2 - Группа авторов


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and shell vibration frequencies was studied in Bagdasaryan (1986), Koreshkova and Khromatov (2009), Golubeva et al. (2013) and Khromatov and Golubeva (2013).

      We also mention the optimal control problem for continuous systems (Andrianov and Iskra 1991).

      DEEM and its generalizations are important particular cases of high-frequency asymptotics. The effectiveness of this method for analyzing the main types of plates and shells used in engineering practices has been proven through experience. The main advantage of DEEM consists of its simplicity and good compatibility with variational approaches.

      Naturally, DEEM is not a panacea. For example, when considering a mixed boundary value problem with many points of change in the boundary conditions, the method based on the homotopy parameter (Andrianov et al. 2014) seems more suitable.

      Nevertheless, in general, we hope that our review has convinced researchers that DEEM and its generalizations occupied an honorable place in the arsenal of analytical methods for solving the dynamics and stability problems of thin-walled structures.

      Several years ago, Professor I. Elishakoff pointed out that it would be useful to prepare a new review of Bolotin’s method, since his previous review on this topic was written in 1976. We are grateful to him for this idea.

      CONFLICTS OF INTEREST. The authors declare no conflict of interest.

      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?

      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”.

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