Flow-induced vibrations of flat plates are studied in water. An equation of motion of the plate-spring system is formulated incorporating the hydrodynamic loads given by the linearized potential theory, and the unknown, vortex-induced, forcing moments. Considerations of bluff-body wake dynamics show the coefficient of this forcing moment to be a function of the steady-body Strouhal number, the chord-to-thickness ratio, and a self-excitation parameter which contains the transverse body motion. This function is evaluated for plates with different trailing edges using experimental measurements of vibrational amplitude and frequency, and the nature of its dependence on vibration is shown to be equivalent to a negative damping. The poles of the amplitude-response relation are shown to predict the bounds of the zone in which large vibrational (“singing”) motion occurs. Criteria are offered for the design of systems to avoid these self-excited vibrations.

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