# Nonlinear dynamic analysis of a partially fluid-filled tank

## Palavras-chave:

tank, sloshing, nonlinear dynamic## Resumo

The nonlinear dynamic analysis of a partially fluid-filled tank is proposed considering the coupling

between the sloshing phenomena and the flexible tank. Donnell non-linear shell theory is considered to describe a

simply supported cylindrical tank while the fluid is based on the velocity potential theory that describes an inviscid,

irrotational and incompressible fluid. As the fluid is linear, it is possible to consider the velocity potential in two

parts: the first one that describes a flexible cylindrical tank without the sloshing and the second one that considers

the effect of the sloshing in a rigid tank. These hypotheses are guaranteed with a convenient choice of expressions

for the velocity potentials that obey boundary conditions equivalent to these considerations. The equivalent

hydrodynamic pressure is obtained by the velocity potential and applied in the equations of the cylindrical tank as

an external force while the free surface equilibrium equation must also be considered together with the cylindrical

tank’s equation. The set of the final discrete equations to be solved is obtained applying the standard Galerkin

method in the tank’s equations and in the free surface equation, creating a coupled system. First of all, the linear

problem is considered to obtain the natural frequencies for the cylindrical shell (bulging modes) and the sloshing.

Afterward, the dynamic nonlinear analysis takes place with the special attention to the frequency-amplitude

relations, phase-portraits and resonance curves that they evaluate the nonlinear oscillations of the cylindrical tanks.