Nonlinear system identification and control of fluid-elastic vibrations of a cylinder row using bifurcation theory

A row of flexible cylinders in a cross flow undergoes sudden large amplitude vibrations when the flow velocity is increased past a critical value. This change in dynamical behavior can be characterized as a sub-critical Hopf bifurcation that occurs at the critical flow velocity. The hysteretic behavior of the cylinder amplitude with flow velocity has resulted in extensive damages to commercial systems such as heat exchangers and nuclear reactors.; In this study, nonlinear system identification and control are used to eliminate the undesired hysteretic region in the fluid-elastic vibrations of a cylinder row. The system identification is effected on single degree of freedom and two degrees of freedom systems using experimental data and bifurcation theory. A nonlinear system identification technique based on the method of harmonic balance (Harmonic Balance Nonlinear IDentification - HBNID) is extended to multi-degree of freedom systems and its performance is evaluated on two theoretical models. HBNID performs well in cases where the structure of the nonlinearities; in the physical system is known and a large number of harmonics of the periodic motion are available. HBNID, however, does not capture all the characteristics in experimental systems where the nonlinearities are not well known or experimental noise corrupts higher harmonics. In order to improve this aspect, center manifold and normal form analysis and a rough experimental estimate of the unstable limit cycle amplitude are used to obtain a set of constraints which are enforced on the unknown parameters. This new methodology, called Bifurcation Theory System IDentification or BiTSID, is used along with experimental data to obtain models for the single degree of freedom and two degrees of freedom systems. These models match the experimentally observed response very well and also capture the bifurcation behavior of the systems. Various analyses of these models are performed to fully understand their bifurcation characteristics outside the experimental region.; An optimal, adaptive, nonlinear control strategy is devised to eliminate the hysteresis region due to the sub-critical Hopf bifurcation. This is done by using the center manifold and normal form analysis to identify the minimal nonlinear feedback that converts the sub-critical bifurcation behavior into a super-critical one. The control feedback is applied to just one of the vibrating cylinders and worked successfully on the two degree-of-freedom system with three different nonlinear feedbacks.; The system identification methodology (BiTSID) developed in this study is a general technique that can be applied to any physical system with a limit cycle response. The minimal control strategy devised is useful in the nonlinear control of a sub-critical Hopf bifurcation into a super-critical Hopf bifurcation.; Finally, the two degrees-of-freedom system is extended to a seven degree-of-freedom system which is then numerically analyzed. The response of this seven degrees-of-freedom system is shown to exhibit spatially localized limit cycles and co-existing limit cycles observed in the experiments.