Page 49 - Marine Structural Design

26 Part I Structural Design Principles

2.2.5 Statistical Determination of Wave Heights and Periods
In the time-domain analysis, the significant wave height H, is defined as the average height of
the highest one-third of all waves, and it is also denoted as HI,, .

(2.16)

where N is the number of individual wave heights and Hi is a series of wave height ranked
from highest to lowest. In the frequency domain analysis, the significant wave height H, is
defined based on the zero moment,m,, which is the area under the energy density spectrum
curve.

H,=4& (2.17)
In the time-domain analysis, the root-mean-square (rms) wave height H, is defined as

(2.18)

In the frequency domain analysis, H,, is defined as.
H,,, =2& (2.19)

In the time-domain analysis, the maximum wave height H,, is the largest value of the wave
heights in a record. In the frequency domain analysis, the most probable maximum wave
height H,, is defined by Longuet-Higgins (1 952) for a narrow band of the wave spectrum as,

(2.20)

In the time-domain analysis, the mean zero-upcrossing period TOv2 defined as the total length
is
of time divided by the number of zero upcrossings in the record. The mean crest period T,,, is
calculated as the total length of time divided by the number of crests in the record.
In the frequency domain analysis, the mean wave period is defined as

T,,, = 2n- m0 (2.21)
MI
(2.22)

2.3 Ship Response to a Random Sea
2.3.1 Introduction

The six degrees of freedom motions of ships nd floating systems are illustrated in Figure 2.5.