Water Wave Control by a Pitching Plate

Abstract

A new idea for controlling water waves is presented in this paper. A submerged pitching plate is suggested as an active wave controller, and its feasibility is theoretically investigated. The two-dimensional problem is formulated to deal with a fully submerged pitching plate fixed at its middle point scattering an incoming monochromatic wave, and the frequency of pitching is kept the same as that of the monochromatic wave. The method of matched eigenfunction expansions is used to analyze the amplitudes of reflected and transmitted waves with and without pitching. The variation of wave reflection and transmission versus the dimensionless water depth, length of plate, and its depth of submergence is discussed. The characteristics of the pitching plate are like a fixed plate and still very sensitive to its submerged depth and physical dimensions. The pitching plate has its high performance by controlling the phase and magnitude of pitching. Based on the linear wave theory, the wave force and moment are estimated, and their characteristics are illustrated in this paper. It is found that pitching has no influence on wave force but induces additional moment on the plate.