Simulation of Flexural Dynamics of a Slender Ship undergoing Heave and Pitch

A simulation model for the flexural dynamics of a slender ship undergoing heave and pitch in regular waves is presented. The heave and pitch motions are found from the strip theory of Gerritsma and Beukelman [1] which is known to be experimentally validated. It is assumed that the ship structure is sufficiently stiff so that bending deformations do not significantly alter the wave field and hence the hydrodynamic loads determined from the strip theory may be used as inputs to the flexural model. The flexural dynamics is modeled by applying the hydrodynamic loads to a lumped-mass beam model and the equations of motion are formulated using the methods of Kane and Levinson [2]. The flexural model can capture large deformation behavior and is tested by demonstrating convergence to a known analytic solution. The model is easily implemented and may be used to evaluate time histories of bending moment responses to waves as well as to slamming events if the slamming load is known or estimated. Some typical results are presented.