Motion of a Solid Body with a Cavity Containing a Multilayer Ideal Fluid*

The motion of a solid body with a cavity containing a heavy multilayer ideal incompressible fluid is considered using a linear problem statement. An algorithm for obtaining a system of ordinary differential equations describing the forced vibrations of the multilayer fluid in the solid body moving in a certain way is given. Using a cylindrical cavity of arbitrary cross-section as an example, this system of equations is analyzed in the cases of complete and partial filling of the cavity, translational vertical and horizontal displacements of the body, vibrations of the body as a physical pendulum. It is shown that in the case of a cavity in the form of a rectangular parallelepiped when the perturbing force acts horizontally parallel to its lateral sides, the waves are excited on the free and inner surfaces of the multilayer fluid, which are asymmetric about the symmetry planes of the rectangular parallelepiped. If the cavity is axisymmetric, then only one-node vibrations of the free and inner surfaces are excited. The frequency equation of free oscillations of multilayer fluid is analyzed for a number of partial cases: full and partial filling of the cavity, infinitely high depths of filling, two-layer and three-layer fluids. For identical layers of the fluid (constant depth of filling of layers and constant ratio of the densities of the layers) the analytical solution of the frequency equation is obtained and analyzed.