Flow-induced vibration of long-span gates part I: Model development

Abstract

This paper presents a theoretical analysis of the flow-induced flexural vibration of long-span gates at small openings. Such a gate is in most cases long enough to be subject to elastic vibration due to its bending flexibility in the streamwise direction. This vibration is accompanied by a variation of the flow rate from under the gate. If the skin-plate of the gate and the floor include an angle smaller than 90°, the gate acts as a “press-shut device”, and the variation of flow rate may cause severe self-excited gate vibrations. The streamwise gate vibration induces surface waves in the upstream channel and fluctuations of the hydraulic pressure due both to flow rate variations and the push-and-draw effect of the gate movement. The pressure induced by the flow-rate variation will supply energy to the vibrating gate, whereas the pressure induced by the push-and-draw effect will consume energy from the vibrating gate. If the energy supply due to the flow-rate variation exceeds the energy consumption due to the push-and-draw effect and to mechanical damping, the gate becomes self-excited. The calculation of the hydrodynamic pressure induced by an arbitrary gate motion is based on a potential theory developed by Rayleigh for dissipative-wave radiation problems. With the aid of this theory, the flow-fluctuation phenomenon is reduced to an initial-boundary value problem which can be solved by making use of mathematical techniques such as Fourier series, Fourier integrals and Laplace-transforms. The equation of gate motion is derived in the form of a second-order differential and integral homogeneous equation, the dimensionless variety of which yields the basic parameters determining the vibration characteristics. The dimensionless equation of motion includes an integral fluid term describing the effects of added mass, fluid damping and fluid excitation, as an acceleration and a velocity term. The major characteristics of gate vibration are discussed in terms of the solutions for the hydrodynamic pressures acting on the gate. Calculated data on fluid damping and fluid excitation, finally, reveal the tendency of long-span gates to undergo flow-induced vibrations.