Springing Analysis of Elastic Vessels in Head and Oblique Seas Including Nonlinear Effects Due to Second Order Diffraction Pressures

Abstract

The wave-induced vibration of the ship hull, commonly called springing, may not produce extreme stresses, but it is likely to have a direct effect on fatigue-life estimates due to its high frequency content. This research investigates the second order contribution to the springing bending moment from the sum frequency of incident ocean waves in both head and oblique seas. The computer program developed here extends the ABS SSRS (Ship Spring Response System) program to oblique seas using Troesch’s oblique sea linear diffraction theory [1]. The theoretical calculations for forward speed are modified by an empirical factor to correlate more closely with experimental results. An example calculation on a Bulk Carrier was performed for different heading angles. For one such representative sea state, the overall increase to the total bending moment from the nonlinear, sum-frequency excitation is found to be less than 12%. However, the nonlinear springing (RMS) increases the total RMS springing over the linear springing by more than 5 times in some stations, which has significant implications for fatigue studies. A sea state sweep study (using ITTC spectrum) also shows the springing effects are highly sea state dependent. Overall, springing effects decrease as zero crossing periods increase, which indicates springing is important in sea states with short waves and becomes less significant in sea states with long waves.