Analysis and reversal of dry and hydroelastic vibration modes of stiffened plates

This work describes the theoretical modal analysis model for the stiffened bottom plate of a tank that is filled with fluid having an undisturbed free surface. In the analysis model, the effects of bending, transverse shear and rotary inertia in both the plate and the stiffener are considered. Analytical results concerning the natural frequencies of the stiffened plate correlate well with experimental modal testing (EMT) results for above the second mode. To overcome the complexities in the modal analysis of the fluid–structure interaction, the Mindlin plate theory and the potential flow theory are applied; the velocity potential is also expressed using double finite Fourier transforms. Additionally, a parametric study was also performed for eigenfrequencies of the plate with a stiffener, in terms of the ratio of the depth of the stiffener to the thickness of the plate and that of the width of the stiffener to the thickness of the plate. Analysis results revealed the phenomenon of “mode reversal”, i.e. the first and second mode shapes of the plate with a deep stiffener in contact with air and water, respectively, are reversed. An occurring condition of “mode reversal” is derived and verified by both finite element analysis and EMT.