Transient Sloshing in Partially Filled Laterally Excited Spherical Vessels

Three-dimensional transient liquid sloshing in a nondeformable spherical container filled to an arbitrary depth and subjected to an arbitrary lateral external acceleration is investigated. The problem solution is achieved by using the linear potential theory in conjunction with the Mehler-Fock transform of general order in the toroidal coordinate system, resulting in a pair of coupled integro-differential equations, which are discretized using Gauss-Laguerre quadrature formula and then solved by appropriate numerical schemes. The transient sloshing response to a real seismic event is calculated and discussed. Also, a ramp-step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver. The effects of the fill depth on the time histories of the horizontal hydrodynamic forces acting on the spherical container are examined. Limiting cases are considered, and good agreements with available analytic and numerical solutions and experimental data are obtained.