CABLE RESPONSES
263
unstable solutions yn(r). Those results are shown in Figure 10.8, which is sometimes called the Heines-Strett diagram. If the parameter set (ôn,3n) lies in the
cross hatched régions, yn(r} is stable, but if this parameter set is elsewhere, the
responses are unstable. Further studies hâve shown that the addition of light
damping increases the parameter range for stability where the cross hatched
régions are extended to the broken lines of Figure 10.8.
Example Problem 10.2. Shown in Figure 10.9 is a landing ship-tank (LST),
spread- moored in the Gulf of Mexico. For this ship, O’Brien and Muga (1964)
took simultaneous measures of the spectra for the surface wave height and the
tension forces in the restraining lines. The measured wave height spectra are
shown in Figure 10.10, and the measured longitudinal force response spectra for
port bow chain No. 2 are shown in Figure 10.11. The problem is to explain
the reason for the double peaks in these bow chain force response spectra. Are
those peaks due to transverse or parametric excitation, or do they arise from
some other reason?
PLAN
VIEW
Figure 10-9 A spread mooring configuration for an LST in the Gulf of Mexico.
The data for the overall mooring restraint System and the ship s surge and
sway frequencies were given in Example Problems 2.10 and 5.5. Pertinent data
on bow chain No. 2 are as follows. The actual unit mass of this chain is increased
by 3 percent to give its virtual unit mass.
m = (1.03)mo = 1.03(35 lb/ft)(32.2 ft/sec2)"1 = 1.12 lb-sec2/ft2
£ = 465 ft, length;
Po = 30,000 1b;
Pi = O.5Po
The first step is to calculate the natural frequencies of the bow chain. From
équation (10.22) and the preceding data, it follows that
w =:^Æ = 2L4®® = l.llnrad/sec, n = l,2,-" £ V m
465 V 1-12
For résonance due to transverse excitation, one would expect peak bow
responses near cun or near 1.11, 2.22, ... rad/sec. Since Figure 1 .1 I s >ow
significant peaks at these frequencies, it is concluded that there is no igm
bow chain résonance response.
263
unstable solutions yn(r). Those results are shown in Figure 10.8, which is sometimes called the Heines-Strett diagram. If the parameter set (ôn,3n) lies in the
cross hatched régions, yn(r} is stable, but if this parameter set is elsewhere, the
responses are unstable. Further studies hâve shown that the addition of light
damping increases the parameter range for stability where the cross hatched
régions are extended to the broken lines of Figure 10.8.
Example Problem 10.2. Shown in Figure 10.9 is a landing ship-tank (LST),
spread- moored in the Gulf of Mexico. For this ship, O’Brien and Muga (1964)
took simultaneous measures of the spectra for the surface wave height and the
tension forces in the restraining lines. The measured wave height spectra are
shown in Figure 10.10, and the measured longitudinal force response spectra for
port bow chain No. 2 are shown in Figure 10.11. The problem is to explain
the reason for the double peaks in these bow chain force response spectra. Are
those peaks due to transverse or parametric excitation, or do they arise from
some other reason?
PLAN
VIEW
Figure 10-9 A spread mooring configuration for an LST in the Gulf of Mexico.
The data for the overall mooring restraint System and the ship s surge and
sway frequencies were given in Example Problems 2.10 and 5.5. Pertinent data
on bow chain No. 2 are as follows. The actual unit mass of this chain is increased
by 3 percent to give its virtual unit mass.
m = (1.03)mo = 1.03(35 lb/ft)(32.2 ft/sec2)"1 = 1.12 lb-sec2/ft2
£ = 465 ft, length;
Po = 30,000 1b;
Pi = O.5Po
The first step is to calculate the natural frequencies of the bow chain. From
équation (10.22) and the preceding data, it follows that
w =:^Æ = 2L4®® = l.llnrad/sec, n = l,2,-" £ V m
465 V 1-12
For résonance due to transverse excitation, one would expect peak bow
responses near cun or near 1.11, 2.22, ... rad/sec. Since Figure 1 .1 I s >ow
significant peaks at these frequencies, it is concluded that there is no igm
bow chain résonance response.