Earthquake-induced sloshing in a rigid circular tank

The present paper describes the sloshing of a liquid in a rigid circular cylindrical tank subjected both to harmonic and to irregular base motion. 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 case of energy dissipation of a real fluid is then treated by a simple extension to this, which involves an assumption of dissipation at the free surface and a corresponding modification to the free surface boundary condition. In order to treat earthquake-induced motions, this solution is then extended to (i) the stochastic response to a base motion which describes a stationary random process; (ii) the time-domain response to a specified base acceleration record; and (iii) a simplified method of estimating maximum forces using a modal analysis and involving earthquake response spectra. The estimation of hydrodynamic damping is briefly considered, and example applications are provided.