FORCED LIQUID OSCILLATIONS IN COAXIAL SHELLS

Abstract

There are many unsolved problems regarding the strength of coaxial shells partially filled with an ideal incompressible fluid. In this regard, it becomes necessary to consider problems associated with studying the dynamic interaction of coaxial shells with a liquid. The problems of unsteady deformation of such shells are insufficiently studied and need more attention. Having determined the region of integration, supposed that the fluid is incompressible or weakly compressible, and using the boundary element method, we can solve the corresponding boundary value problem. Note that the fluid motion is vortex-free and this allows us to use the velocity potential, which satisfies the Laplace equation and the boundary conditions, both on rigid surfaces of the shell and on the fluid free surface, since the motion of the fluid volume is completely determined by the motion of its boundary surface. A description of the liquid behavior with the free surface can be summarized in set of dependencies, which are conditions of a kinematic and dynamic nature. Kinematic conditions can be considered as mechanical bonds that impose restrictions on the variations of the unknowns, dynamic conditions follow from the variational principle of Hamilton−Ostrogradsky, as natural ones. The fluid pressure will satisfy the Cauchy−Lagrange conditions. The walls of the shell can be considered as rigid ones. The natural frequencies of the fluid are essentially less than the natural frequencies of the elastic shell with the liquid. The effect of surface tension can be neglected, that is, the effect of surface tension on fluid vibrations is small. The calculations are performed, which make it possible to determine the frequencies and modes of liquid sloshing in coaxial shells. The forced oscillations of the fluid under the influence of horizontal harmonic, impulse and seismic loads are considered.