Analytical solution of capsizing moments in ship chamber under pitching excitation

Abstract

As the core structure of the shiplift, the ship chamber is a typical rectangular container with filling water depth less than 0.1. Even small pitching excitation could produce large liquid sloshing and significant capsizing moment, and lead to a catastrophic overturning accident. As a basis of dynamical modeling and simulation of the shiplift, a fluid dynamic model is presented to predict the capsizing moments based on the Housner theory. Assuming a time-harmonic pitching excitation, the potential solution reflecting dynamic characteristics between pitching excitation and the fluid free surface oscillation angle is expanded analytically. A series of engineering formulas for the capsizing moments, including impulsive and convective parts, are then imposed. Comprehensive numerical analysis further extends the applicability of formulations to the cases for most of ship chambers or other rectangular tanks with similar filling water depth. The validation of proposed scheme is extensively demonstrated through comparison with other theoretical method and experimental results, and the interaction between the forcing frequency, the capsizing moments and fluid natural frequency has been qualitatively descripted. The results exhibited that the present model has accurate description under the conditions of small pitching angles and only considering the capsizing moments coming from the convective pressures can ensure high accuracy in engineering design.