An Analytical Model for Unanchored Fluid-Filled Tanks Under Base Excitation

A set of equations is derived describing the dynamic response of cylindrical liquid storage tanks under horizontal ground excitation. The structure consists of a flexible cylindrical tank with a roof and a bottom plate and rests on a flexible ground through a rigid foundation. Portion of the base of the tank may separate from and lift off the foundation during ground motion. The solution of the hydrodynamic problem is first found in closed form. Then, Hamilton’s principle is applied and the equations governing the behavior of the coupled fluid/structure/ground system are derived. During this procedure, the base uplifting is modeled by an appropriate rotational nonlinear spring placed between the base of the tank and the foundation.