Raynovskyy I. An asymptotic modal Narimanov-Moiseev theory of the damped steady-state sloshing in an upright cylindrical tank

The Thesis develops methods of analytical mechanics and asymptotic methods of nonlinear mechanics for studying the damped steady-state sloshing in an upright cylindrical tank. By introducing (an infinite number) of the generalised coordinates and velocities, by applying variational principles of analytical mechanics and the Euler-Lagrange equations of the second kind in the Miles-Lukovsky's form, as well as by using the Narimanov-Moiseev asymptotics, the original free-surface problem reduces to a system of ordinary differential equations with respect to the introduced generalised coordinates. The system effectively approximates resonance motions of the present mechanical system when the frequency of periodic motions of the tank is close to the lowest natural sloshing frequency. Accounting for the viscous damping, periodic solutions of the system are constructed and analysed. This makes it possible to describe all classes of the steady-state sloshing in the tank during its orbital three-dimensional resonance motions.