Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019


-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6


15 20 Time t U = 0.5, V = 0.03


Figure 8: Comparison of the vibration amplitude between the free span with a 45° slope considering gravity and ignoring gravity (


t[15, 30]).


0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35


0 2 25


g = 9.8 m/s2 g = 0


0.05 during t ∈ [15, 16]. The mode shapes also clearly reveal the difference between the two different cases.


30


-8 -7 -6 -5 -4 -3 -2 -1 0 1


0.0 γ = 45° 1 4 6 8


Dimensionless frequency f U = 0.5, V = 0.03


0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40


0 2 γ = 45° 1 10 (a)


-8 -7 -6 -5 -4 -3 -2 -1 0 1


0.0 0.2 0.4 Time t U = 0.8, V = 0.035


(a) g = 9.8 m/s2 (b) g = 0


Figure 10: Instantaneous displacement during t ∈ [15, 16] 4 6 8


Dimensionless frequency f U = 0.5, V = 0.03


(a) g = 9.8 m/s2 (b) g = 0


Figure 9:Frequency analysis of the free span with a 45° slope.


The mode shapes of free-spanning pipelines with U = 0.8, V = 0.035, and γ = 45° are shown in Figure 10, where (a) is depicted when gravity is considered and (b) is depictedwhen gravity is ignored. The lines are plotted for a time internal of


10 (b) 4.2 NATURAL FREQUENCY


To calculate the natural frequency of the free-spanning pipeline system using GITT, both the external and internal flow velocities are set as zero. A random noise with an amplitude of order O(10-3) is applied to the dimensionless transverse displacement z. Calculations are done respectively for the free-spanning pipeline with a slope angle of 0°, 15°, 30° and 45° respectively. The spectral analysis of the midpoint vibration under the above- mentioned conditions are provided in Figure 11.


(b) 0.6 0.8 1.0 0.2 0.4 Time t U = 0.8, V = 0.035 (a) 0.6 0.8 1.0


©2019: The Royal Institution of Naval Architects


A-329


Displacement-to-diameter ratio z PSD PSD


Displacement-to-diameter ratio z Displacement-to-diameter ratio z


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