Theoretical and experimental studies of vibrations of the solid half-cylinder having a cavity filled with a layered fluid

Further exploration of outer space is not possible without energy industrialization. For the industrialization of outer space, Russian and American experts are considering the possibility of creating orbital refueling stations and space refueling stations for future flights to the Moon, Mars and other planets. The proposed article presents the formulation of the problem, the solutions and the results of studies of the dynamic characteristics and stability of small oscillations of a solid, simulating a space tanker, whose fuel tank contains a cryogenic liquid. A distinctive feature of a cryogenic liquid is the low temperatures and various densities of fluid particles observed in the processes of storage and operation, which greatly complicates the study of hydrodynamic problems. In the article, the cryogenic fluid is modeled by layers of immiscible liquids. In the work, the equations of motion of a rigid body with a cavity containing three immiscible incompressible ideal liquids and performing a plane motion are obtained. The formulation of the problem of small oscillations and stability of motion of a rigid body with a cavity filled with such a layered fluid is given. The areas of stability of the motion of a solid semi-cylinder with a cylindrical cavity filled with three immiscible liquids are investigated. The article also presents the results of an experimental study of oscillations of a half-cylinder with two immiscible liquids.