Study on the Coupled Torsional and Flexural vibration of Ships with Large Hatch Openings (2nd Report)

Abstract

Torsional and horizonta1 vibrations of ships usua11y occur together as coupled vibrations because of the asymmetry about any horizontal axis of the cross section of a ship. Especia11y in the case of ships with large hatch openings, such as container ships, torsional and horizontal vibrations must be tightly coupled, because the shear centre is located far apart from the centre of gravity of the cross section. In order to clarify the main feature of the coupled torsional and horizontal vibrations of those ships, theoretical study was made on the coupled torsional and flexural vibrations of a uniform bar of open cross section with only one axis of symmetry, taking into account the effects of torsional rigidity and shear deflection of the members of the bar in the same manner as was described in the first report. The usefulness of the results of theoretical study was confirmed by experiments in which vibration tests were conducted on nine models made of steel and aluminium. The conclusions obtaind are summarized as follows: (1) Due to the coupling between torsional and flexural vibrations, a bar of open cross section has two types of norma1 modes of vibration which are distinguished by the terms "vibration of type 1" and "vibration of type 2". (2) When the bar vibrates in a steady state, the apparent centre of rotation of the cross section is a fixed point which is inherent for each type of vibration mentioned above. (3) The effect of torsional rigidity and the effect of shear on the natural frequencies of the bar can be approximately treated in the same manner as for the case of simple torsional vibration described in the first report. (4) The torsional rigidity and the shear deflection of the members of the bar have little effect on the normal mode patterns of vibration of the bar in the wide range of the factors λ and β.