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A streamwise bending vibration mode of a Tainter gate skinplate involving rotational vibration about a horizontal rotational axis along the weir-plate surface was identified through post-failure modal analysis on one of the remaining Folsom dam gates. This modal deflection of the skinplate of a gate pushes and draws the water in the reservoir inducing hydrodynamic pressure fluctuations (termed the push-and-draw pressure). To analyze this push-and-draw pressure, a simplified analytical model was formulated. The model consisted of a rigid, vertical, flat weir-plate undergoing rotational vibration with its horizontal rotational axis along the weir-plate surface above a horizontal bed with a vertical step down at the gate position. Results from the theoretical analysis (based on dissipative wave radiation theory) are presented in terms of non-dimensional parameters, such as the Froude number and a reduced height of the skinplate rotation center. The validity of the analysis was confirmed by forced vibration experiments using a rigid, vertical, flat weir-plate. To extend the theoretical model to loading on circular-arc skinplates, pressure measurements were made on an inclined circular-arc skinplate undergoing forced vibration above a curved dam crest with a vertical step down on the upstream side. From these measurements, an empirical correction to the analysis was developed to account for the curved surfaces of both the gate and the dam crest. Integrating the pressure loading over the submerged skinplate surface area permitted the determination of the hydrodynamic load on the skinplate. As a result of this study, a method has been developed for estimating the pressure fluctuation due to streamwise vibration on any skinplate undergoing streamwise rotational vibration. The method was used to estimate the loading on a circular arc skinplate as a function of the reduced vibration amplitude and the Froude number. |
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