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

Abstract

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. The reliability of the results obtained is substantiated by comparing them with the known data for the case when the annular gap is completely filled with an ideal fluid. The influence of the fluid level and the size of the annular gap on the eigenfrequencies and the corresponding vibration modes of coaxial shells under a variety of boundary conditions is analyzed. It has been demonstrated that partial filling leads to splitting of natural vibration frequencies, while a decrease in the filling level facilitates the growth of their minimum values. It is shown that the appearance of mixed vibrational modes, both in the meridional and circumferential directions depends on the size of the annular gap.