Study on the Coupled Torsional and Flexural Vibration of Ships with Large Hatch Openings (5th Report) : Coupled Torsional and Horizontal Vibration of a Bar with Open Cross Section in the Free Surface of Water

Abstract

This paper describes some theoretical analyses for the entrained water of a bar vibrating in a free surface. Inertia coefficients, C_H and C_T, of the rectangular sections of various b/d ratios are calculated for the horizontal and the torsional vibrations. In the case of coupling between torsional and horizontal vibrations in the free surface of water, the concept of added virtual mass and added mass moment of inertia for a vibrating bar requires the existence of a definite point in the cross section, at which both the added mass for horizontal vibration and the added mass moment of inertia for torsional vibration are to be concentrated so that the kinetic energy expression for the surrounding water may not have coupling terms of horizontal and torsional motion. This definte point will be called the "centre of entrained water" in the present report, and the position of the point is calculated for the rectangular sections of various b/d ratios. By the use of these numerical informations, analyses for the coupling between torsional and horizontal vibrations of the models of rectangular section in a free surface show good agreement with the experimental results.