Dzyuba V. Interaction of the cylindrical shell and spherical body in compressible liquid

The dissertation is devoted to an efficient approach for solving problems on spherical and cylindrical (rigid or the thin elastic shell) bodies interaction in compressible liquid. The internal axis symmetrical (the cylindrical shell is loaded by the acoustic medium and contains the spherical body, which vibrates on its axis) and external (the interaction of the cylindrical and spherical bodies in the infinite acoustic space) tasks are considered. The investigation is based on the possibility of representing particular solutions of the Helmholtz equation written in cylindrical coordinates with the help of particular solutions in spherical coordinates, and vice versa. It is permit the general solution to be written both in the cylindrical and spherical coordinate systems with the help of the superposition technique and the boundary conditions on the surfaces of the every body to be satisfied. As a result, the problems are reduced to investigating and solving infinite systems of linear algebraic equations for defiining unknown constants, which consist in the equation solutions, written as a series with the separate variables. The hydrodynamic characteristics of the liquid and the shell deformation characteristics have been defined.