Viscous Fluid in Tank under Coupled Surge, Heave, and Pitch Motions

Abstract

A tank might be simultaneously excited by surge, heave, and pitch ground motions during earthquakes. A time-independent finite-difference method is used to intensively study the combined effects of surge, heave, and pitch motions on sloshing viscous fluid in a rigid, rectangular tank. A complete fully nonlinear free-surface condition is used in the analysis. The numerical results are validated by the existing reported results. The evolution of the velocity vectors are described and discussed in detail. The coupled surge and heave and combined surge, heave, and pitch motions would enhance the free-surface stability during the transition period, during which the free surface variation ceases and sloshing begins in the opposite direction. No clear eddies are generated during a surge motion as they are during a heave motion. While the tank is experiencing pitch motion, a clear clockwise eddy occurs during the transition period, when the slope of the surface is negative. However, the eddy is counterclockwise when the slope is positive. A comparison between the surface elevation with combined surge, heave, and pitch motion and that of the superposition of separated excitation is made. The coupling effects are significant, and simultaneous surge and pitch motions should be included during a real earthquake analysis. The dominance of the frequency of excitation, ωx, on the frequency of the sloshing displacement is presented when ωx is less than the first fundamental frequency of water in tank, ω1. The first fundamental frequency dominates the frequency of the sloshing displacement throughout the sloshing when ωx is greater than ω1.