Nonaxisymmetric Vibrations of a Shell of Revolution Partially Filled with Liquid

We propose an algorithm for finding the frequencies and modes of natural vibrations of the shells of revolution partially filled with liquid. The problem of perturbed motion of a liquid is solved under the assumption that its free surface remains flat and perpendicular to the axis of the shell. The solution is based on the use of the method of decomposition of the domain of integration of the equations of the theory of shells in combination with the variational method and the approximate construction of the inverse operator for the hydrodynamic part of the problem. We construct a generalized functional with respect to displacements of the shell for which the conditions of conjugation of the solutions in subdomains are included in the natural boundary conditions. The obtained numerical results are compared with the available exact solutions of the problem under consideration with regard for the wave motions of liquid in a shell in the form of circular cylinder. © 2016, Springer Science+Business Media New York.