Optimal modal vibration suppression of a fluid-conveying pipe with a divergent mode

This study deals with the divergence characteristics of pipes conveying fluid and explores the applicability of active modal vibration control for suppressing the associated excessive structural vibration. The Timoshenko beam theory is used to establish the system equation of motion. The analysis is based on the finite element method. Active modal control technique is developed in this work for pipes conveying fluid with a flow speed exceeding the critical one. Optimal independent modal space control (IMSC) is applied for the design. For pipes conveying super-critical flow speed, as considered in this work, the systemʹs eigenvalues have both real and complex roots, which must be dealt with in a different way from what has been established in the literature. A weighting matrix with finite weights is applied for the control of complex modes, whereas a weighting matrix with an infinite weight is used for controlling the divergent mode, with roots being real. From this study, it is demonstrated that the control approach proposed in this work can ensure closed loop stability. The mode switching scheme of directing control to the mode which has higher modal response is found to be beneficial in reducing the overall structural vibration of the fluid-conveying pipe.