Coupling dynamic analysis of a liquid-filled spherical container subject to arbitrary excitation

Using spherical coordinates, the coupling nonlinear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O variational principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.