Dynamics and Control, 11, 187–201, 2001  2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Optimal Control of Flow-Induced Vibration of Pipeline SAROJ K. BISWAS sbiswas@vm.temple.edu Department of Electrical and Computer Engineering, Temple University, Philadelphia, PA 19122, USA N. U. AHMED School of Information Technology & Engineering, Department of Mathematics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5 Editor: M. J. Corless Received July 12, 2000; Revised August 8, 2001; Accepted August 8, 2001 Abstract. We investigate self-excited lateral vibration of a pipe due to an internal flow. The stability boundary of fluid velocity is expressed in terms of the system parameters, such as, pipe material density and rigidity, and fluid density, etc. To maximize the fluid transport efficiency, it is necessary to maximize the flow velocity while minimizing the lateral vibration of the pipe. We use the integral minimum principle of Pontryagin to find the optimum flow velocity for minimum pipe vibration. The results are illustrated by numerical simulation. Keywords: flow-induced vibration, pipeline vibration, fluid flow optimization, Pontryagin’s minimum principle 1. Introduction Structural failure due to flow-induced vibration is a common problem affecting the per- formance and reliability of heat exchangers. It is estimated that electric utility industries spend thousands of dollars every year in repair or replacement of tubes in steam genera- tors and other heat exchangers damaged by vibrations. Under certain conditions fluid flow inside a pipe can initiate vibrations of the pipe. If the vibration intensity is large enough, pipes can strike against each other or against their supports causing structural fatigue or complete failure. Flow-induced vibration also occur in transcontinental oil pipelines caus- ing damage of support structure or cracks of the pipelines leading to costly shutdown. In marine applications, pipes can start to vibrate in the presence of external cross-flow of water caused by ocean current. Flow-induced vibration of pipes has been a subject of considerable research in the last four decades. Many of these studies [13,15,17,19,22] are directed towards studying practi- cal vibration problems of heat exchanger tubes in steam generators in conventional power plants and nuclear reactors. Good heat exchanger design requires understanding of vibra- tion mechanisms, and possible fluid-elastic instability. Frequently, methods of analysis [5,12,14,21] involve the use of finite element models and their eigen-solutions. Nonlinear models [8,14,24] have also been used for analysis of self-excited vibration of pipes.