different bandwidths, named Process 1 and Process 2, used in the simulation by JF. 
Dalzell.° The deviation from the Rayleigh distribution in Figs. 12.8 to 12.11, and the 
relation of the standard deviation of roll op to that of input o,, in Fig. 12.12 shows the 
extent of nonlinearity. The applicability of the method was also discussed. 
10° 
P(A) RAYLEIGH 
PRESENT THEORY 
to2L  PRESENTTHEORY__ | 
WITH LINEAR RE- 
STORING MOMENT 
10° 
0 0.1 0.2 0.3 0.4 
Fig. 12.8. Probability density function for amplitude A: 
a=0, b=1, oy = 0.036, 2 = 0.90, 
Process 3. (From Roberts.®") 
DALZELL’S SIMULATION 
ESTIMATES 
a=0 
i bel 
0 0.1 020.3 04 0.5 0.6 p 
Fig. 12.9. Cumulative probability distribution for amplitude A: 
a=0, b=1, oy = 0.036, Q = 0.90, 
Process 3. (From Roberts.®") 
352 
