Flow Induced Vibration of Long Span Gates : Derivation of Equation of Motion

Abstract

To study the flow induced small-amplitude-vibration of long span gates under small gate openings which are inclined toward the downstream side, this study presents an analytical method to derive the hydrodynamic pressure induced by an arbitrary gate motion. In the analysis, the Rayleigh's potential theory developed for dissipative-wave radiation problems is applied to reduce the flow fluctuation phenomena to an initial-boundary value problem which can be solved by making use of mathematical techniques such as Fourier series transform, Fourier integral transform and Laplace transform. Consequently, the equation of gate motion is derived in the form of a homogeneous differential-integral equation.