Quadratic strip theory for high-order dynamic behavior of a large container ship with 3D flow effects

Springing is the resonance phenomenon of a ship hull girder with incoming waves having the same natural frequency of the ship. In this study, a simple and reliable calculation method was developed based on quadratic strip theory using the Timoshenko beam approach as an elastic hull girder. Second-order hydrodynamic forces and Froude–Krylov forces were applied as the external force. To improve the accuracy of the strip method, the variation in the added mass along the ship hull longitudinal direction, so called tip-effect, was considered. The J-factor was also employed to compensate for the effect of three-dimensional fluid motion on the two-node vibration of the ship. Using the developed method, the first- and second-order vertical bending moments of the Flokstra ship were compared. A comparative study was also carried out for a uniform barge ship and a 10,000 TEU container ship with the respective methods including the J-factor and tip-effect.