DEPLOYMENT OF AN OTEC PIPELINE
277
segments during deployment. This end condition is
#MM) _ dv(0,t)
-K~dT(10.125)
The transverse motion at the bottom is minimized by the addition of a ballast
mass Mo which is pinned at x = L. Thus
d2v(L,t)
d^v(L.f)
ib’ml.r;
f
"■
LI~â^- ■ -
(10.126)
which express, respectively, the condition of zéro end moment and the compatibility of the transverse shear force at the pin with the motion of the ballast
mass.
At location x the average tension load on the cross section dépends on two
dead weight terms and on the barge heave motion, H(t). That is,
P(x,t) = Mrg + (L - x)mig + (L - x)mH(t) + M0H(t)
(10.127)
where M^g is the ballast weight in water, mAg is the weight per unit length of
the pipe and its contents in water, and 7T(t) is the barge heave accélération. It is
asumed that Hit) is approximately the same at the top and bottom of the CWP
since the natural period of longitudinal pipe oscillations (Ti) is significantly
smaller than the shortest excitation period (T^). For a Steel pipe 1000 m long,
î) = 0.3 s is smaller by about an order of magnitude than the shortest realistic
excitation period of T2 = 3 s.
Pipe Excitations by Barge and Waves
Assume that the motions of the barge from which the pipeline is deployed
are completely determined by the océan waves. That is, the barge motion is not
affected by the pipe motion, which is a reasonable assumption since the barge
mass and the wave forces on it are both much larger than the pipe mass and
the pipe’s wave forces. Choose the modified Pierson-Moskowitz spectral density
function for the sea surface élévation g(t), or
= AuT5e~B^
(10-128)
where A and B are constants and the wave frequency has the range
< w <
UN- Partition the spectrum into N components for which the nth component
is S^(wn). As discussed by Borgman (1969), the sea surface wave amplitude at
each central frequency mn — nAm is given by
rç(mn) = [2S>n)A^]1/2, n = 1.2,...,X
(10.129)
where the bandwidth Am is sufficiently small.
The heave motion of the barge is thus
H(t) = 52
+
(10.130)
n—1
277
segments during deployment. This end condition is
#MM) _ dv(0,t)
-K~dT(10.125)
The transverse motion at the bottom is minimized by the addition of a ballast
mass Mo which is pinned at x = L. Thus
d2v(L,t)
d^v(L.f)
ib’ml.r;
f
"■
LI~â^- ■ -
(10.126)
which express, respectively, the condition of zéro end moment and the compatibility of the transverse shear force at the pin with the motion of the ballast
mass.
At location x the average tension load on the cross section dépends on two
dead weight terms and on the barge heave motion, H(t). That is,
P(x,t) = Mrg + (L - x)mig + (L - x)mH(t) + M0H(t)
(10.127)
where M^g is the ballast weight in water, mAg is the weight per unit length of
the pipe and its contents in water, and 7T(t) is the barge heave accélération. It is
asumed that Hit) is approximately the same at the top and bottom of the CWP
since the natural period of longitudinal pipe oscillations (Ti) is significantly
smaller than the shortest excitation period (T^). For a Steel pipe 1000 m long,
î) = 0.3 s is smaller by about an order of magnitude than the shortest realistic
excitation period of T2 = 3 s.
Pipe Excitations by Barge and Waves
Assume that the motions of the barge from which the pipeline is deployed
are completely determined by the océan waves. That is, the barge motion is not
affected by the pipe motion, which is a reasonable assumption since the barge
mass and the wave forces on it are both much larger than the pipe mass and
the pipe’s wave forces. Choose the modified Pierson-Moskowitz spectral density
function for the sea surface élévation g(t), or
= AuT5e~B^
(10-128)
where A and B are constants and the wave frequency has the range
< w <
UN- Partition the spectrum into N components for which the nth component
is S^(wn). As discussed by Borgman (1969), the sea surface wave amplitude at
each central frequency mn — nAm is given by
rç(mn) = [2S>n)A^]1/2, n = 1.2,...,X
(10.129)
where the bandwidth Am is sufficiently small.
The heave motion of the barge is thus
H(t) = 52
+
(10.130)
n—1