Practical approach of linear hydro-elasticity effect on vessel with forward speed in the frequency domain

Abstract

In this study, a practical approach to incorporate forward speed and hydro-elasticity effect in the frequency domain is developed. By utilizing the discrete-module-beam (DMB) method, flexible structures are partitioned into multiple rigid bodies that are connected by beam elements. The forward speed effect is taken into consideration in the multi-body hydrodynamics through the slender body and low uniform flow speed approximation, which is called the uniform flow approximation (due to no steady perturbation coupling term considered). By implementing the uniform flow approximation into the multi-body hydrodynamics formulation and then coupling it with the DMB method, any multi-rigid-body radiation–diffraction simulation tools can be extended to solve the linear hydro-elasticity problem with forward speed effect. The present numerical results compare well with published experimental and computational results, including a more direct but much more time-consuming FEM–BEM coupling method. By using the developed computer program, the increase of elastic response and change in dynamic bending moment are assessed for various wave lengths and forward speeds in the case of Wigley hull. The occurrence of hydro-elastic resonance at the first bending mode at certain forward speed is illustrated for a typical operational sea state. The forward speed also changes the wet mode shape, dynamic elastic response, and dynamic bending moment and its distribution along the ship. Encounter frequency, convective term in the pressure formulation and the m-terms contribute to their changes. The effect of local structural damage on the modal characteristics and the resulting hydro-elasticity is also investigated It needs to be noted that due to several approximations (e.g., uniform flow and free-surface approximations), care should be exercised when applying the proposed method.