Study on the Coupled Torsional and Flexural Vibration of Ships with Large Hatch Openings (1st Report) : Torsional Vibration of a Bar with Open Cross Section

Abstract

Torsional vibration of ships with large hatch openings, such as container ships, must be dealt with by bending-torsion theory including torsional rigidity GJ and warping rigidity EГ, because they usua11y behave as bars with open cross section. This paper presents the results of thoeretical and experimental study on the torsional vibration of the uniform free-free bar of open cross section with two axes of symmetry ,the purpose of which is to find the effect of torsional r1gidity and warping rigidity and also the effect of shear on the torsional vibration of the bar mentioned above. The theoretical results are compared with the experimental results, and the following conclusions are obtained; (1) In order to calculate natural frequency of torsional vibration of a bar exactly, it is necessary to take into account the torsional rigidity GJ, the warping rigidity EГ and the effect of shear. (2) In the higher mode of vibration, the effect of torsional rigidity on the natural freqency can be genera11y neglected. If λ<1, the effect of torsional rigidity might be neglected for a11 modes except one-node mode. (3) In the higher mode, however, the effect of shear on the natural frequency increases. This is exactly the same as the effct of shear on the flexural vibration of beams. (4) One-node vibration is governed mainly by the torsional rigidity GJ, while the vibrations above two-node are governed mainly by the warping rigidity EГ. In the case of one-node vibration, the effect of shear can be neglected.