The theoretical analysis of coupled-mode self-excited vibration of hydraulic gates is developed in the present paper. The theory is applied to the 87-ton Tainter gate at the Folsom Dam, which according to eyewitness testimony, experienced flow-induced vibrations and failed in l995. In its original design, the Folsom Tainter gate possessed two significant vibration modes. One mode was a whole gate rotation around the trunnion pin, while the second mode was a streamwise bending vibration of the skinplate. For certain upstream water levels, these two modes can couple with each other through hydrodynamic forces and inertia torques, producing self-excited vibration. The equations of motion for the small amplitude coupled-mode vibration are derived in non-dimensional form, revealing the non-dimensional parameters governing the vibrations and the hydrodynamic forces. The characteristics of this coupled-mode self-excited vibration are obtained through approximate numerical solutions, derived by iterative numerical calculations of the equations of motion. In addition, examination and physical explanations for vibration trajectories and energy transfer from the fluid motion to the gate vibration are presented. The theory, along with measured in-air frequencies, mode shapes and damping ratios, is used to generate stability diagrams of the original Folsom gate designs.
- Vibration, Flow-induced, Tainter gate, Coupled-mode, Self-excited, Equations of motion.
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