Linear springing responses are numerically evaluated in the design spiral for ultra large containership and large ore carrier. Numerical methods used in the present work are based on the modal superposition and the coupling of whole ship finite element model (3D FEM model) in structure regime and three-dimensional hydrodynamic model (3D panel model) in hydrodynamic regime. Springing-induced as well as wave-induced vertical, horizontal and torsional moments produced on the hull girders were calculated for a wide range of wave encounter frequencies. It is shown that for the ultra large containership the first and second modes of the combined torsional and horizontal vibrations of the hull contributed to the first peak of springing response and its energy is large enough to have impact on the structural behavior of the ship. On the contrary, for the large ore carrier the torsional modes of hull vibrations were negligible at high wave frequencies so that they impose little effect on the spring response of the ship.
The importance of hydro-elasticity has emerged in ship design practice because of excessive hull girder vibrations which are frequently reported to be partly responsible for the fatigue damage and reduction of the vessel life in seagoing ships. It is well known that this high order of hull vibrations is partly attributed to springing response which is caused by the resonance between structural natural frequencies of a ship and wave encounter frequencies. According to the rapid increase in size and speed of modern cargo carriers, the structural natural frequencies tend to approach the range of the wave encounter frequencies. This context forced the ship designers in shipyard to pay attention to the numerical calculations of springing response and the inclusion of the springing-induced response in the structural design of the ship hulls.