Liquid vibration modeling in prismatic tanks with quarter baffles

Abstract

Free vibrations of liquid in a rigid prismatic tank with vertical cross partitions are considered. These partitions divide the tank into four compartments. The partitions make it possible to reduce the amplitude of liquid sloshing in the tank under suddenly applied external loads due to earthquakes, terrorist attacks, emergencies, etc. It is assumed that the fluid is perfect and incompressible, and its motion is vortex-free. Under these conditions, there is a velocity potential that satisfies the Laplace equation. A non-leak condition is applied on the sides, bottom and partitions of the tank. On a free surface, kinematic and dynamic conditions are set. The kinematic condition is that the points of fluid that are on the free surface at the initial moment will remain on that surface for the entire subsequent motion. The dynamic condition is the equality of the fluid pressure on the free surface to the atmospheric pressure. An analytical solution of the boundary value problem for the Laplace equation is obtained for the case of the tank with a square bottom. The free surface oscillations have been found to be symmetrical. It should be noted that the oscillation patterns in each compartment are the same. The frequencies of free oscillations of the fluid in the tank with the cross partitions are increased in comparison with similar frequencies of oscillations of the prismatic tank without partitions. The frequencies obtained and the modes of natural oscillations of the fluid free surface allow us to solve the boundary value problem in case of sudden external loads. In this case, the velocity potential and the function describing the behaviour of the free surface are represented as the series according to the modes of natural fluctuations of the fluid free surface. Therefore it is possible to prevent the unwanted resonant frequencies at exploitation and transportation by designing prismatic tanks in a particular way.