Natural vibrations of a rotating circular cylindrical shell containing fluid

The finite element method is used to study the natural vibrations of rotating circular cylindrical shells containing a fluid, which rotates with the same angular velocity as the shell. Centrifugal and Coriolis forces acting on the rotating shell are considered. The geometric stiffness matrix that takes into account the influence of the initial circumferential tension caused by centrifugal forces is obtained by solving the static problem. The fluid motion is described in the framework of the potential theory. The results of numerical experiments performed for shells with different boundary conditions and geometric dimensions are given.