Abstract Elastically suspended Tainter gates (radial gates) may induce a rigid-body vibration around the trunnion pin, accompanied by discharge variations. The fluctuating discharge causes a fluctuation of pressure acting on the gate which may induce gate vibrations. Such a small-amplitude flow-induced vibration of Tainter gates is described by a homogeneous integral-differential equation. In this study, this homogeneous equation is approximately solved to obtain solutions for the excitation ratio (negative damping ratio) and vibration frequency. The solutions are given for a variety of parameters, such as basic Froude number, mass ratio and equivalent damping ratio. The predictions are compared with experimental data on Tainter-gate vibrations. A design criterion is presented, which ensures the stability of Tainter gates with respect to a significant source of self-excited vibration that was previously ignored.
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