136
SINGLE DEGREE OF FREEDOM STRUCTURES
(5.110). With a suitable choice of Ç, the damping constant is determined from
équation (5.107). Then with a choice of wave height and Cm, together with
the ftxed System characteristics of geometry and inertia, ail of the coefficients
in équation (5.111) are known. The System parameters used to compute these
coefficients are listed in Table 5.3.
Table 5.3 System Parameters for the SALM Buoy
Buoy diameter
Buoy height
Buoy moment of inertia
Cable angle
Cable location on buoy
Cable material parameter
Cable material parameter
Damping factor
Drag force location on buoy
Flow coefficient
Water depth
Water weight density
Wave frequency range
Wave height
D = 240 in.
2hd = 1320 in.
Jo = 5-57 x 109 lb-in.-sec2
hc = 960 in.
a0 = 2.82 x 104 Ib/in.
b0 = 1.34 x 105 lb/in.3
Q = 0.05
hd = 660 in.
Cm = 2
d = 1200 in.
pg — 0.0372 lb/in.3
0 < uj < 15 rad/sec
H = 120 in.
Numerical Results and Conclusions
Numerical solutions to équation (5.111) were obtained using a step-by-step
Runge-Kutta intégration procedure, subjected to the at-rest initial conditions
of 0(0) = 0(0) = 0. The discrète values of buoy rotation 0, as well as its angular
velocity and angular accélération, were calculated at a time step sufficiently
small to show response behavior accurately. This time step was chosen as onetenth of the smaller of either the natural period To = 2tt/w0 of the équivalent
hnear System, or of the excitation period T = 2tt/w.
Shown in Figure 5.14 as a function of the wave forcing frequency w is the
a soluté value of the horizontal amplitude of displacement at the top of the buoy:
2ha8a where 0Q is the computed amplitude of rotation. This figure displays three
important features. First, the amplitude behavior is similar to the simpler
nonhnear hard (cubic) restraint System, Figures 5.9 and 5.10: an amplitude
ur e that leans to the right. Second, the ratio of the peak dynamic response to
«lw static response in Figure 5.14 is 5.4/0.5 = 10.8, which compares favorably
• response ratio of 10 for a linear System with £ = 0.05, shown in Figure
’ ’ i ?ird’ m
range °f wave frequency 7.8 < w < 8.8 rad/sec, the buoy’s
amplitude >s multi-valued. indicating the occurrence of jumps.
SINGLE DEGREE OF FREEDOM STRUCTURES
(5.110). With a suitable choice of Ç, the damping constant is determined from
équation (5.107). Then with a choice of wave height and Cm, together with
the ftxed System characteristics of geometry and inertia, ail of the coefficients
in équation (5.111) are known. The System parameters used to compute these
coefficients are listed in Table 5.3.
Table 5.3 System Parameters for the SALM Buoy
Buoy diameter
Buoy height
Buoy moment of inertia
Cable angle
Cable location on buoy
Cable material parameter
Cable material parameter
Damping factor
Drag force location on buoy
Flow coefficient
Water depth
Water weight density
Wave frequency range
Wave height
D = 240 in.
2hd = 1320 in.
Jo = 5-57 x 109 lb-in.-sec2
hc = 960 in.
a0 = 2.82 x 104 Ib/in.
b0 = 1.34 x 105 lb/in.3
Q = 0.05
hd = 660 in.
Cm = 2
d = 1200 in.
pg — 0.0372 lb/in.3
0 < uj < 15 rad/sec
H = 120 in.
Numerical Results and Conclusions
Numerical solutions to équation (5.111) were obtained using a step-by-step
Runge-Kutta intégration procedure, subjected to the at-rest initial conditions
of 0(0) = 0(0) = 0. The discrète values of buoy rotation 0, as well as its angular
velocity and angular accélération, were calculated at a time step sufficiently
small to show response behavior accurately. This time step was chosen as onetenth of the smaller of either the natural period To = 2tt/w0 of the équivalent
hnear System, or of the excitation period T = 2tt/w.
Shown in Figure 5.14 as a function of the wave forcing frequency w is the
a soluté value of the horizontal amplitude of displacement at the top of the buoy:
2ha8a where 0Q is the computed amplitude of rotation. This figure displays three
important features. First, the amplitude behavior is similar to the simpler
nonhnear hard (cubic) restraint System, Figures 5.9 and 5.10: an amplitude
ur e that leans to the right. Second, the ratio of the peak dynamic response to
«lw static response in Figure 5.14 is 5.4/0.5 = 10.8, which compares favorably
• response ratio of 10 for a linear System with £ = 0.05, shown in Figure
’ ’ i ?ird’ m
range °f wave frequency 7.8 < w < 8.8 rad/sec, the buoy’s
amplitude >s multi-valued. indicating the occurrence of jumps.