Abstract Summary
Modern ships can easily exceed 400m in length. At this size, the flexural response of the ship can be significant, and the natural frequencies can be dangerously close to the energetic region of typical ocean waves. Container ships with relatively little deck stiffening are particularly flexible, especially in torsion. This makes them vulnerable to both whipping and springing responses. Whipping is the term used to describe a transient, resonant, structural response of the hull caused by the sudden impact of a large wave. This is a nonlinear process which cannot be captured by strictly linear models but can be an important component of the Ultimate Limit State. Springing is the term used to describe resonant hull vibrations induced by continuous wave forcing, and this can be induced by both linear and nonlinear wave forcing. Springing is important for the prediction of fatigue loading. This talk will describe some of our recent work on numerical modelling of the hydro-elastic response of ships. We apply potential flow theory to describe the interaction between the waves and the ship. Several levels of modelling are applied, starting with a linear method where the hydrodynamic loading is computed using the concept of generalized modes, and the ship structure is approximated as a slender Euler or Timoshenko beam. Hydrodynamic calculations are performed using our in-house high-order finite difference-based open-source tool OceanWave3D-Seakeeping. The linearized problem for the flexural response can be formulated either in the global coordinates (Newman’s method) or in a local coordinate system fixed to the instantaneous rigid-body position (Malenica’s method). We show that the two formulations result in different inertia and hydrostatic contributions but give the same response, and are thus both consistent and equally valid. Several examples will be given to illustrate this for simple geometries. Examples will also be given comparing calculations to experimental measurements for several geometries at both zero and non-zero forward speed. Work is also in progress on more accurate, nonlinear models for the structural response of the ship and extending the hydrodynamic analysis to nonlinear wave loading.
