The Effect of Shallow Water upon the Natural Frequencies of Hull

Abstract

An experiment has been carried out at the laboratory of Prof. Kumai to find the effect of shallow water upon the added virtual mass of the cylinder models of the typical sections of cargo ship, especially great emphasis being placed on the effect of breadth-draught ratio.
As the result of this experiment, the increase fraction of the added virtual mass due to shallow water (c) was disclosed as follows :
c=1.1 β³ (b/d) (d/h) ^2.2
where, β : area coefficient of section b : breadth of section
d : draught h : depth of water
In the case of ship's form, the increase-fraction (C) deduced when applying the above formula for lines of hulls can be expressed as follows :
C=1.19 (B/d) (d/h) ^2.2C_b
where, B : moulded breadth
C_b : block coefficient
The natural frequencies at shallow water can be estimated according to the method described in the auther's previous paper : “The Estimation of the Principal Natural Frequncies of Hull”, and the coefficients of the increased added virtual mass necessary for the frequencies calculation are given in Fig. 3.
After comparison was given to the measured data and the calculated ones, this method has been confirmed to be satifactory for practical use.