Shell-plate interaction in the free vibrations of circular cylindrical tanks partially filled with a liquid: The artificial spring method

The free vibrations of a circular cylindrical tank partially filled with an inviscid and incompressible liquid with a free surface orthogonal to the tank axis are analytically studied. The tank is modelled by a simply supported circular cylindrical shell connected to a simply supported circular plate by an artificial rotational distributed spring of appropriate stiffness. The plate is considered to be resting on a Winkler elastic foundation. The effects of the free surface waves and the hydrostatic liquid pressure are neglected. The bulging modes (where the tank walls oscillate with the liquid) of the structure are investigated and the solution is obtained as an eigenvalue problem by using the Rayleigh-Ritz expansion of the mode shapes and then minimizing the Rayleigh quotient for coupled vibrations. The effects of the liquid level inside the tank, of the stiffness of the Winkler foundation and of the spring stiffness at the shell-plate joint are investigated for shallow and tall water-filled tanks. Comparison with available results is also given. © 1997 Academic Press Limited.