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The importance and usefulness of a particular calculation method is determined by its wide application when studying practically important systems and phenomena. From this point of view, the importance of DEEM is not in doubt.

From the very beginning, DEEM was originated by Bolotin for the analysis of overhead power lines (Bolotin et al. 1958).

DEEM was used to obtain estimates for the density of natural frequencies of shallow shell vibrations (Gavrilov 1961b; Bolotin 1963; Stearn 1970; Zhinzher and Khromatov 1971, 1972a, 1972b; Moskalenko 1972, 1975). This is very important during the study of random vibrations of elastic structures (Bolotin 1966; Birger and Panovko 1968; Moskalenko 1968; Bolotin 1984; Elishakoff et al. 1994).

The influence of the magnetic field on the distribution of plate and shell vibration frequencies was studied in Bagdasaryan (1986), Koreshkova and Khromatov (2009), Golubeva et al. (2013) and Khromatov and Golubeva (2013).

A lot of research devoted to the problems of aeroelastic stability and supersonic flutter can be mentioned (Zhinzher 1983; Zhinzher and Kadarmetov 1984, 1986; Dubovskikh et al. 1996).

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.