Abstract
A method is proposed for constructing a solution to the problem of natural oscillations of shells of revolution described by surfaces of rotation of the second order. The initial equations of shell theory are arranged in a sequence that allows one to calculate the unknowns in an iterative process. The system of the first two momentless equations and the first two equations of infinitesimal bending in the proposition that their inverse operators can be constructed, can be reduced to a single equation for the vector of tangential deformations. The possibility of such a representation is due to the research of V.Z. Vlasov shells of revolution, the meridians of which are described by second-order curves. It is shown that the results of calculating the natural frequencies of vibrations of loose shells given in the well-known reference book on strength, stability and vibrations are incorrect.
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