Analogies between the classical problem on vibrations of two coupled bodies and the nonclassical problem on propagation of plane waves in theory of two-phase mixtures - Rushchitsky, J.J. (Reports of the National Academy of Sciences of Ukraine, 2021)
In order to identify analogies in the procedures of analysis, two problems are described and commented on: the classical problem (problem V) on harmonic vibrations of two interconnected rigid bodies suspended on the springs, and the nonclassical problem (problem W) on the propagation of plane longitudinal waves in the twophase elastic mixture. A number of analogies are constructed between these problems, which are described in the form of 6 steps of the comparative analysis of problems V and W, each of which corresponds to a specific analogy. Emphasis is placed on the usefulness of the observed analogies for the analysis of the problem of waves. Thus, it is shown that the theory of two-phase mixtures in its development in the field of wave theory can successfully use the analogies from the corresponding problems of the theory of vibrations of two coupled oscillating systems. The more general fact follows from the analogies shown that the mechanism of mutual aid in the theory of vibrations discovered almost 100 years ago by Academician Mandelstam extended its influence to the theory of waves during this time.