КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ СТІЙКОСТІ РУХУ РІДИНИ В РЕЗЕРВУАРАХ ПІД ДІЄЮ ПЕРІОДИЧНИХ НАВАНТАЖЕНЬ

The paper proposes a method for studying the stability of fluid motion in reservoirs under periodic forcing. It is assumed that the fluid inside the reservoir is an ideal and incompressible, and its motion due to applied loads is non-vortex. The velocity potential is determined from the boundary value problem for the Laplace equation. To obtain an integral equation for subsequent numerical implementation, the third Green’s formula is employed. This led to the need of solving the system of singular integral equations for unknown basis functions, representing the modes of fluid vibrations in the rigid shell. The fulfillment of the dynamic boundary condition allowed obtaining a system of differential equations, constituting a set of Mathieu equations. The stability of the solution is investigated. It reveals the possibility to indicate zones and parameters of unstable motion.