a+a-=at+/8/x-B -wodx. (10.21) 
Comparing this expression with Eq. 10.2 for the deterministic case gives 
£ 1.6 
x0 = (SJ 085 
Ga— 20%. (10.22) 
namely for our interest, xo appeared almost equal to the significant amplitude for the 
stochastic case. 
P. Kaplan” used this general result and calculated the ship’s rolling for the same 
example that this author solved by the perturbation method as shown in the next section. 
Kaplan found that the result checked very well with this author’s result. 
10.3 PERTURBATION METHOD 
10.3.1 Trial for Ship’s Rolling 
This author showed”? the results of the computation of nonlinear rolling using the 
perturbation method. The effect of nonlinear damping was investigated first. One degree 
of freedom rolling is expressed as 
Ip +N\d + No)? +Kig = M, (10.23) 
d + 2ad + Bidld + wih = mit). (10.24) 
Starting with a 0 order approximation ¢o (when f = 0), that is linear, 
do + 2abo + WewWo = mit), (10.25) 
go= | hg ym(t —T) m(t)at = | hggm(T) m(t—T)at. (10.26) 
Here hg,m(T) is the impulse response of the 0 order, namely linear approximation @o to the 
exciting moment m(t), 
285 
