Bogun R. Identifying the dynamic characteristics of the moving liquid volume, partially restricted absolutely rigid and flexible surfaces

Thesis is devoted to interaction of an ideal and incompressible liquid in moving tanks. The liquid free surface is covered by constructive devices appearing as flat elastic plates or flexible membrane, which is clamped to the walls of the container. A general linear mathematical model of the system motion is constructed. It takes the form of a system of ordinary differential equations with respect to generalized coordinates characterizing the motion of liquid, elastic element and the solid body. Finding the coefficients of the motion equations is associated with solutions of the homogeneous boundary problem on natural oscillations of the "liquid–elastic element" system and inhomogeneous problem on the Stokes–Joukowski potential. Two methods to find solutions of the hydroelastic problem on the natural liquid oscillations in an axisymmetric tank are proposed. The first method is based on the construction of an approximate solution using a sequence of solutions of the auxiliary inhomogeneous boundary Neumann problems associated with the Laplace equation in the liquid occupied domain. The second method is based on expansion of eigenfunction of an auxiliary spectral problem with a parameter in boundary conditions. Based on the obtained results, a series of particular problems are solved. We analyze the convergence of the proposed algorithms as well as identify the main effect of the constructive devices on the dynamic behavior of the liquid in mobile and static tanks.