Ship Hull Vibration Research Articles

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

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.

On the Estimation of Natural Frequencies of Vertical Vibration of Ships

The paper deals with the estimation of natural frequencies of the vertical vibration of ship hull, taking into account the recent investigations on the effects of fineness of the hull, shear deflection and rotatory inertia and the virtual inertia coefficient of the water. Some empirical factors obtained from the observations on board actual ships are shown. Here are also put forward new empirical formulae for estimating inertia coefficient of the water surrounding a vibrating ship based on the data obtained from several ship-shaped models.

On the Effects of Shear Deflection and Rotatory Inertia upon the Damping of Ship Vibrations in the Higher Modes

The relation between the logarithmic decrement of the damping and the natural frequencies of a free-free beam which is in higher modes of flexural vibration is theoretically investigated here, taking into account as parameters the shear deflection and rotatory inertia factors as well as the inner damping force due to the normal and tangential viscosities of the material or structure of the beam. The external damping force is ignored. It is concluded that the shear deflection and the tangential viscosity of the beam have more conspicuous effect than the rotatory inertia and normal viscosity. In regard to the rotatory inertia, the logarithmic decrement increases with the increase of rotatory inertia, though the natural frequency decreases. The results of the investigation will be applied to the response calculation in the higher mode of the ship hull vibrations excited by the propeller blade force.

On the Three-dimensional Correction Factor for the Virtual Inertia Coefficient in the Vertical Vibration of Ships

In the present paper, the local reduction factor for the two-dimensional virtual mass in the vertical vibration of Lewis-formed ship hull is attempted to calculate with the aid of measurements of hydrodynamical pressures at the special points of a contour of each section of the hull along her length under water line of a model ship.As a result, the considerable reduction of the local factors at the near from both ends of a cylinder which previously calculated by the author was clearly confirmed in the present experiments. However, the results from the models of ship like beam were obtained with different tendency that the distribution of the local reduction factor is almost constant along ship length. Consequently, we may safely assume that the total reduction factor, J, may be applied for three-dimensional correction of the virtual mass in the vertical vibration of a ship hull as usual method, however it will be expected that considerable local reduction of the three-dimensional factor on the virtual mass in the horizontal vibration of ships appears at the near from both ends.

An Accelerometer for Measuring Ship Hull Vibrations

This paper describes an accelerometer, which has been developed for measuring the vibrations of ships' hulls. High sensitivity is obtained by the use of wire resistance strain gauges, of high resistance. When an accelerometer with d.c. excitation is used in conjunction with an a.c. amplifier, a balancing system is not required; furthermore, the accelerometer may be used in any plane without adjustment. Recording is by means of a pen recorder.