Analysis of spatial vibrations of coaxial cylindrical shells partially filled with a fluid

This work is devoted to a numerical study of natural vibrations of horizontally oriented elastic coaxial shells with the annular gap completely or partially filled with a compressible viscous fluid. The solution is searched for a three-dimensional formulation of the examined dynamic problem using the finite element method. The fluid motion is described in the acoustic approximation in terms of the velocity potential. The corresponding equations together with the boundary conditions, related to a full fluid-shell contact, are transformed using the Bubnov-Galerkin method. The hydrodynamic forces are determined from the viscous stress tensor. The mathematical formulation of the problem of thin-walled structure dynamics is based on the variational principle of virtual displacements, which includes the normal and tangential components of forces exerted by the fluid on the wetted parts of elastic bodies. Modeling of the shells is based on the assumption that their curvilinear surfaces are simulated quite accurately by a set of flat segments, the strains of which are determined by the relations of the classical thin plate theory...