Hydrodynamic influence on ship-hull vibration close to water bottom

The problem of a uniform ship-hull girder vibrating vertically close to water bottom is studied. A simple formula for the added mass is found by use of the method of matched asymptotic expansions. Results obtained from the present method and BEM are compared. They are in good agreement in the range considered here. The obtained added mass is used to predict the natural vibrations of a uniform beam vibrating close to water bottom. Numerical values show that the effects of shallow water are significant. The first- and second-order frequencies of the ship hull studied in this paper in deep water are about 1.4-3 times higher than those in shallow water.