The method of integral equations in the problems of studying oscillations of shells partially filled with liquid - Myronenko, Maria (Bulletin of V.N. Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems», 2021)
G-force reaching several g affect the stability of the launch vehicle in the launching phase. The mathematical modeling methods are used to study the longitudinal vibration stability of liquid-fueled launch vehicles in the launching phase. The paper presents the modeling of small oscillations of fluid motion in a rigid, partially filled shell of rotation. The modeling is based on the developed mathematical model: fluid is supposed to be ideal and incompressible, fluid motion being vortexless, velocity potential gradient being fluid velocity. The conditions for the velocity potential at the boundaries of the computational domain are determined. The kinematic boundary condition and dynamic boundary condition on the free surface and nonpermeability condition on the bottom and side surfaces of the tank are fulfilled. The solution of the differential equations system for the boundary conditions has been obtained. The liquid sloshing in a low gravity has been investigated and the boundary conditions have been generalized. In the dynamic boundary condition the surface tension is accounted for. The assumed mode method has been developed to solve problems of free and forced oscillations of shell structures with compartments filled with liquid. The system of differential equations relative to the elastic movements of the structure and the active liquid pressure is obtained. For its solution three sets of basic functions have been used. The gravitational component in the singular equation system in the problem of sloshing in a rigid shell is taken into account. The cases of control points being positioned on the liquid free surface, as well as on the shell surface are considered. The solution of the system of equations determines the velocity potential.