Numerical modeling of eccentric cylindrical shells partially filled with a fluid

The paper is devoted to a numerical analysis of the dynamic behavior of horizontally oriented eccentric shells, interacting with a flowing fluid, which completely or partially fills the annular gap between them. The solution to the problem is developed in a three-dimensional formulation using the finite element method. When modeling elastic solids, we proceed from the assumption that their curved surface is accurately approximated by a set of plane segments, in which the strains are determined using the relations of the classical theory of plates. The motion of an ideal compressible fluid is described by the wave equation, which, together with the impermeability condition and the corresponding boundary conditions, is transformed using the Bubnov–Galerkin method. The mathematical formulation of the dynamic problem of thin-walled structures is based on the variational principle of virtual displacements. The assessment of stability is based on the calculation and analysis of complex eigenvalues of a coupled system of equations. The verification of the model is accomplished with reference to a quiescent fluid by comparing the obtained results with the known solutions. The influence of the size of the annular gap and the level of its filling with a fluid on the hydroelastic stability threshold of rigidly clamped shells is analyzed at different values of shells eccentricity. It has been shown that for eccentric shells, a decrease in the level of filling leads to an increase of the stability limits. The dependence of the critical flow velocity on the deviation of the inner shell from concentricity has been established.