7.6. IRREGULAR (2-D) WAVE GENERATION
417
=
0
= sinh[(fcm + Afc/)Z]
for I > 0
for I < 0
(7.233)
Z»2 =
0
62= sinh[(fcm - Afc/)/]
for I > 0
for I < 0
(7.234)
Similarly, 71 and 72 in Eqn. 7.231 are found from
71 =
71 = cosh[(fcm +
] — (h +
+ △£/) sinh[(fcm +
]
for I > 0
for I < 0
(7.235)
72 =
1
for I > 0
72= cosh[(fcm— △&/)/] —(h +/)(fcm — At/) sinh[(fcm - △&/)/] for I < 0
(7.236)
Of course, the subscript m is replaced with n when evaluating the functions
Pn and Qn.
For an irregular wave train consisting of several hundred short-wave
components, it is necessary to sum up all possible component-pair combinations to get the long-wave board displacement, i.e.,
N
N
xlbM = £ E
(n — m)=l m—m *
(7.237)
Nnm2(0
where m * = f * /f0 and f * is the lowest frequency in the short-wave spectrum and fo is the frequency interval in the Fourier decomposition of the
irregular wave train.
Finally, the total wave board displacement is determined as the
sum of the first-order short-wave control signal plus the second-order long
wave control signal, or
(7.238)