Vibrations of base plates in annular cylindrical tanks: Theory and experiments

In this paper, the bulging modes (i.e., modes where the walls oscillate moving the liquid) of the flexible bottom annular plate of an otherwise rigid annular cylindrical container are studied. The tank has a vertical axis and is partially filled with liquid, so that the free surface of the liquid is orthogonal to the tank axis. The volume occupied by the liquid is delimited by two coaxial rigid cylinders and the liquid deformation potential is obtained by using variables separation. First, by using the simplifying hypothesis that the mode shapes of the plate in contact with the liquid (wet modes) are the same in vacuo, the approach based on the non-dimensionalized added virtual mass incremental (NAVMI) factor is applied, so that all numerical computations can be made non-dimensional. Second, the accuracy of this method is checked by using the Rayleigh-Ritz method, which removes the restrictive hypothesis on the wet mode shapes. Finally, several experimental modal analyses were performed on two different test tanks filled with different water levels in order to verify the accuracy of the theoretical results. (C) 1998 Academic Press Limited.