COUPLED BOUNDARY AND FINITE ELEMENT METHOD FOR STABILITY ANALYSIS OF LAUNCH VEHICLE

Abstract

The methods of potential theory were applied in the research, which made it possible to reduce threedimensional problems to the solution of surface singular integral equations [7]. We started with a thorough analysis of the resulting singular integrals and establishing the type of their singularities [8,9]. After developing an effective method for solving the resolving system of singular integral equations, the natural frequencies of fuel tanks were determined. Further, forced oscillations of partially filled tanks were considered. The cases of stability loss are studied, when the amplitude of oscillations of the liquid free surface sharply increases. This phenomenon occurs when the driving force frequencies coincide with the frequencies of natural oscillations. Also very topical is the case of parametric resonance, which is typical for tank oscillations under the action of a vertical force with a frequency that is a multiple of the lowest natural one.