Earthquake-Induced Sloshing in Vertical Container of Arbitrary Section

Abstract

The sloshing of a liquid in a rigid vertical cylindrical tank of arbitrary section subjected both to harmonic and to irregular base motion is described. Initially, the boundary value problem for the case of an inviscid fluid and a harmonic base motion is solved on the basis of linearized potential flow theory. The solution is based on an eigenfunction expansion method in which a set of boundary integral equations involving a suitable Green's function are solved for each mode. This solution is then extended to the case of energy dissipation of a real fluid, by assuming this to occur at the free surface. Further extensions to a stationary random base motion, to the time-domain response to a specified base acceleration record, and to the estimation of maximum forces using a modal analysis and involving earthquake response spectra are then indicated. Comparisons are made with closed-form solutions for circular and rectangular tanks, and more general example applications are provided.