Earthquake-induced sloshing in vertical container of arbitrary section

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.