416
CHAPTER 7. LABORATORY WAVE GENERATION
F12 — KnmiJmJn 4" Ai * An)
(7.225)
with
_ ________________ M2 f(h + l)_________________
△u>nm[Afc/(h-M)sinh(Afc//i) — cosh(AfcyZi) 4- /3']
(7-226)
where /?' is given by Eqn. 7.223.
The functions Im and Jm contained in Eqn. 7.225 are given below, and
the functions In and Jn are the same except the subscript n replaces m.
j _ ^mkm
(p , Q™ ।
A
z7 227)
m
2sinh(fcm/l) Vm + (h + Z) + km(h + Z) /
(
’
j _
[cosh(fcmh)sinh(A:mh) + kmh] km(h 4- Z)
,
.
m 2sinh(fcm/i)[fcrn(/i 4- Z) sinh(fcm/i) — cosh(£mh) 4- Pm]
The parameter
(or /?n when subscripts are changed) is given by
Pm =
1
for I > 0
Pm = cosh(—kml) for Z < 0
(7.229)
The functions Pm, Qm, and Rm (or Pn, Qn, and Rn with subscripts
changed) in Eqn. 7.227 are given below
1
2
Pm
Qm
sinh[fcm 4- Akfjh] 4sinh[(6m — Akj)h\ 4- Z>2
km+AHtj
km—Akf
£ 71 — cosh[A:m 4- Afy)h] 72 — cosh [(A:™ — Akj)h]
2
( * ™ 4- Akfy
+
(km - Akfy
.
(7.230)
(7.231)
Rm ~ 2
cosh[A:m 4cosh [( km — A kf ) Zi]
hm 4- Afcy
km — ^kj
2km
(7.232)
In Eqn. 7.230, 61 and 62 are determined according to the wave board type
using the equations