Abstract
We propose a variational method for the construction of approximate solutions of the spectral problem of vibrations of two conjugate shells of revolution that are not axially symmetric. The solution of the problem is based on the decomposition of the domain of integration of equations of the theory of shells performed by using the variational method. We construct a generalized functional of displacements of the shell for which the conditions of conjugation of solutions on the common boundary of the introduced subdomains are natural boundary conditions. For a shell formed by a truncated cone and a cylinder, the efficiency of the proposed approach is analyzed and the results of numerical calculations are compared with the available data obtained by the other authors.
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