Modeling of free vibrations of simply-supported submerged horizontal plate

A theoretical approach was applied to investigate the vibrations of a simply-supported horizontal plate. A boundary-value problem was formulated within potential wave theory and was solved by employing the method of matched eigenfunction expansions. The derived analytical solution was applied to determine flow fields and loads on a plate. The derived forces were applied in a motion equation to predict natural frequencies for a simple-supported horizontal plate vibrating in a fluid. The derived model was applied to analyze the effect of the geometry of the plate and its physical and material properties on the free vibration of the submerged plate. The effect of flexural plate rigidity and immersion depth has been taken into account.