Active vortex-induced vibration control of a flexible rod transported in water

This paper addresses the problem of suppression of the vortex-induced vibrations (VIVs) of nuclear fuel rods, transported to the given underwater locations within a nuclear reactor by using a refueling machine (RM). The equations of motion of the considered system are derived by using Hamilton's principle. The finite difference method has been applied to simulate, in MATLAB, the deflections of the fuel rod upon the movements of the RM. Our investigations reveal that the rod vibrates in the lateral and transverse directions, simultaneously, upon a bridge movement in the lateral direction, which coupling results due to the phenomenon of vortex-shedding in water. Also, it is observed that the application of command shaping (i.e., open-loop control) can suppress only the lateral vibrations. Therefore, to simultaneously suppress the lateral and transverse vibrations of the rod, a boundary control law is developed, which controls the movements of the trolley in suppressing the VIVs as the bridge is moved by using a shaped command. Furthermore, Lyapunov-based stability analysis is performed to prove that the closed-loop system is uniformly ultimately bounded considering the influence of distributed hydrodynamic force on the fuel rod.