THREE-DIMENSIONAL EFFECTS ON ADDED MASSES OF SHIP-LIKE FORMS FOR HIGHER HARMONIC MODES

The almost universal method employed for evaluating hydrodynamic added mass for use in ship vibration analysis is F. M. Lewis's classical procedure based on two-dimensional strip theory which does not allow flexure of the hull in cross-sectional planes. Its accuracy may be marginally acceptable for the zero-noded heave mode shape, but deteriorates rapidly with modal order (elastic vibration) due to the increasing influence of three-dimensional hydrodynamic effects or sectional interaction effects which strip theory ignores. This is particularly true in the case of propeller induced vibration of typically 8 to 13 nodes.; In this study, sectional added masses under interactions between neighboring sections are evaluated for modal wave lengths of the order of magnitude of cross-sectional dimensions of the body without solving the entire complicated three-dimensional problem directly. The first part involves an analytic derivation of an expression for added masses attending higher harmonic modes. An approximate solution of modified Helmholtz equation which becomes a singular perturbation problem at small wave lengths is secured. Second, as a bound of the present theory, the modified Helmholtz equation is solved for the long flat plate vibrating at high frequency on the water surface without any limitations on modal frequency. Finally, extensive series of numerical calculations are carried out for ship-like forms.; It is found that when modal wave length is comparable to or shorter than a typical cross-sectional dimension of a body, sectional interaction effects are large which result in considerable reductions in added masses. For a fuller section, the ratio of added mass reduction is greater. Specifically, it is found that added masses are smaller for full sections than for fine sections as modal wave length is decreased. In the limit of vanishing sectional area, the added masses approach to that of flat plate of equal beam.; It is shown that the added mass distribution for a Legendre modal form can be determined from the present theory and that the results agree with the extensive three-dimensional determination of Vorus et al. (6).