Stabilization of a flexible pipe conveying fluid with an active boundary control method

Abstract

A method of stabilizing the self-excited oscillation of a cantilevered pipe conveying fluid because of non–self-adjointness is proposed theoretically and experimentally. Complex eigenvalues denoting the natural frequency and damping of the system vary with an increase in the flow velocity. When the flow velocity exceeds a critical value, the flow-generated damping becomes negative and the pipe is dynamically destabilized. The complex eigenvalues with respect to flow velocity are affected by boundary conditions. We, thus, propose a stabilization control actuating the boundary condition. The stabilization method is carried out by applying a bending moment proportional to the bottom displacement of the pipe. The effect of the proposed control method is shown by investigating the stability for the three lowest modes of the system depending on the feedback gain. It is theoretically clarified that the critical flow velocity is increased by the proposed control method. Furthermore, experiments are performed using a fluid conveying pipe with two piezoactuators at the downstream end. The piezoactuators apply a bending moment at the downstream end of the pipe according to the theoretically proposed method. Experimental results verify that the proposed stabilization method suppresses the self-excited oscillation.