Calculation of Added Virtual Mass and Added Virtual Mass Moment of Inertia of Ship Hull Vibration by the Finite Element Method

Abstract

The added virtual mass and the added virtual mass moment of inertia induced by the vibration of a ship are defined as the equivalent mass and the equivalent mass moment of inertia deduced from the effects of water surrounding a vibrating ship. These equivalent mass and the equivalent mass moment of inertia can be estimated either from the inertia force (or moment) concept or from the kinetic energy concept as long as the ideal fluid is concerned, and the solution of the Laplace's differential equation is required in both cases.This paper, dealing with the problem by the use of the inertia force (or moment) concept, shows that the so-called “finite element method” can be applied, with the aid of a high speed digital computer, to obtain the approximate solution of the Laplace's differential equation with any arbitrary boundary condition. In order to examine the accuracy of this method, the inertia coefficients Cv, CH and CT of vertical, horizontal and rotational vibrations of bars of circular and rectangular cross section are computed first by this method. Then, as an application of this method, the effects on the inertia coefficients of the restricted water and of the bilgekeel are shown numerically.