Hydrodynamic Analysis of Shallow Water Sloshing in Ship Chamber Under Longitudinal Earthquake

Shallow water sloshing-structure interaction under the coupled longitudinal and pitch motions resulted by the longitudinal earthquake directly affects the structural safety of the shiplift. However, no matter in shiplift or other related fields, there is little research on this aspect at present. As a basis of structural dynamics analysis and earthquake resistant design, an analytical method including a developed modal system and new engineering formulas is presented to predict the hydrodynamic moment and force in the ship chamber. Based on the linear modal theory, a modal system describing shallow water sloshing under longitudinal earthquake is developed with infinite set of modal functions. Then, new engineering formulas for calculating the hydrodynamic moment and force are proposed with only retaining the lowest sloshing mode (n=1). Case simulations suggest that the maximum error of hydrodynamic moment and force between n=1 and n=100 are lower than 1.3% and 10.5%, respectively. In addition, the hydrodynamic moment resulting from pressure on the walls can be reasonably ignored, which accounts for less than 0.5% percent of total hydrodynamic moment. With respect to the currently used Housner model, the presented formulas are greatly improved in computational accuracy and rationally supplement the missing part in the seismic design part of the Design code for shiplift.