Natural vibrations of non-circular cylindrical shells partially filled with fluid with sloshing of free surface

The dynamic behaviour of thin-walled reservoirs containing an ideal fluid is investigated taking into account the effects of hydroelastic interaction and sloshing of the free liquid surface. A mathematical statement of the problem is based on the principle of virtual displacements, which makes it possible to consider the pre-stressed non-deformed state of the shell caused by various force factors, for example, by hydrostatic pressure. The strains of the elastic structure are calculated using the relations of the Kirchhoff-Love theory of thin shells. The behavior of compressible liquid is described by the linearized Euler equations for acoustic medium, which are transformed by the Bubnov-Galerkin method. We use appropriate dynamic boundary conditions to take into account waves (or the sloshing effect) on the free surface of the liquid. The behavior of partially filled cylindrical reservoirs of arbitrary cross-sections was analyzed using the developed numerical procedure based on the three dimensional implementation of the finite element method. It has been shown that allowing for free surface sloshing considerably reduces the eigenfrequencies of vibrations of the examined systems. Based on the modal analysis, a classification of the eigenmodes of free surface oscillations of the liquid in the vertical shells of circular and elliptical cross-sections has been done. The analysis has shown that in the case when the vibration frequencies of liquid differ from the vibration frequencies of the shell filled with fluid the frequency spectrum of the system splits into two parts due to sloshing.