Hydroelastic stability of partially filled coaxial cylindrical shells

The work investigates numerically the dynamic behavior of the system, which consists of horizontally oriented, elastic coaxial shells and a flowing compressible fluid partially or completely filling the annular gap between the shells. The solution of the problem is carried out in a three-dimensional formulation using the finite element method. The motion of the compressible non-viscous liquid is described by the wave equation, which together with the impermeability condition and the corresponding boundary conditions is transformed by the Bubnov–Galerkin method. The mathematical formulation of the problem of the dynamics of thin-walled constructions is based on the variational principle of virtual displacements. The simulation of the shell behavior is performed under the assumption that the curvilinear surface is accurately approximated by a set of flat segments, in which the strains are determined using the relations of the classical plate theory. The stability estimate is based on the results of computation and analysis of the complex eigenvalues of the coupled system of equations. The influence of the filling level and the size of the annular gap on the boundaries of hydroelastic stability of rigidly fixed coaxial shells is analyzed. It is shown that a decrease in the filling level leads to an increase in the stability boundaries.