Comparison of finite and boundary element methods in problems of oscillations of a composite shell of revolution with a liquid
Abstract
The phenomenon of sloshing can be described as the movement of the free surface of a liquid contained in a reservoir under the action of a suddenly applied load. Some classifications of free-surface fluctuations in liquids identify three main forms of sloshing: a) longitudinal sloshing, b) vertical sloshing c) rotating sloshing. Sloshing is a phenomenon that is found in a wide range of industrial applications: in containers for storing liquefied gas, fuel tanks of missiles and airplanes, in tanks of cargo tankers. The vibrations of the real tanks are caused by sloshing of the fluid and vibration of the elastic walls. In completely (or almost completely) filled tanks, the free surface cannot experience strong oscillations. This corresponds to launching the launch vehicle. However, in further stages of flight, when the level of liquid aggregate falls, the sloshing effect becomes dominant. It was repeatedly noted that powerful sloshing can lead to a violation of the flight trajectory, as happened, for example, during the launch of the Falcon 1 launch vehicle in 2006, 2007 and 2008. The next important problem in the study of the oscillations of the fuel tanks is the study of the associated hydro-elastic oscillations of the fluid interacting with the elastic walls of the tank. New analytical method and computer technology have been developed for analyzing free and forced vibrations of composite fuel tanks of missiles at different stages of flight: during overloads and in microgravity conditions, including sloshing fuel. The proposed method allows for more accurate analysis of fuel tank oscillations; takes into account the mutual influence of elastic deformations of tank walls and changes in the tank filling levels during missions as well as the shape of the free surface of the liquid, the presence of elastic and rigid damping internal partitions, and the gravity acceleration changes. A mathematical model has been developed for the analysis of fuel sloshing at large amplitudes. The free oscillations of the launch vehicle tanks have been considered.
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