Axisymmetric problem of interaction of the elastic cylindrical shell with the pulsary sphere with presence of a liquid in internal and external domains

The problem on the interaction of a spherical body oscillated by the desired law with a thin elastic cylindrical shell filled by an ideal compressible liquid and submerged in an infinite ideal compressible liquid with other parameters is formulated. The geometrical center of the sphere is located at the cylinder axis. The solution is based on the possibility of representing the particular solutions of Helmholtz's equations for both media written in cylindrical coordinates using the particular solutions in spherical coordinates, and vice versa. As a result of satisfying the boundary conditions on the sphere surface and on the shell surface, the infinite system of linear algebraic equations is obtained to determine the coefficients of expansions of liquid speeds potentials into Legendre polynomials Fourier series. The hydrodynamic characteristics of the liquid filling and ambient the cylindrical volume, as well as the cylindrical shell deflections are determined. The comparison with the problem on sphere oscillations on the axis of an elastic cylindrical shell filled by the compressible liquid (without accounting the external medium) is given.