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Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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A Nonlinear Stability Analysis of Tandem Offloading System
Pages 348-359

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From page 348...
... ABSTRACT In this paper, we analyze the linear and nonlinear stability of a tandem offloading system in wind, current and waves. The wind and current forces are evaluated with the help of published experimental data, while the hydrodynamic coefficients and wave drift forces are carefully estimated by using a three-dimensional singularity distribution method based on potential theory.
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From page 349...
... (2) O 1 Pi External forces consist of the wave radiation force, the viscous force, the wind force, the current force, the wave exciting force, the mooring force and the bow-hawser force.
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From page 350...
... As one can see in these figures, the hawser tension has strong nonlinear characteristics, while the mooring stiffness is nearly constant in the region of small excursion. 2( -~.2 -0.15 -0.1 -o.oS o o.OS 0.1 0.15 0.2 excursion: xIL Figure 2: Restoring force of turret mooring system 2C.
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From page 351...
... The steady-state response corresponds to a large periodic oscillation, which is called the fishtailing motion or limit cycle motion. The nonlinearity of hawser tension and the viscous damping force prevent the eventual blowup of motion.
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From page 352...
... 2SC 350 Figure 8: Yaw motions of FPSO-shuttle tanker system M1l 0 (a=0.2L, l=0.2L, Vw-30m/s, mean wave drift) 0 M22 In order to clarify the entire dynamic response of the mooring system, a stability analysis is required where in terms of design parameters.
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From page 353...
... ~ denotes the ratio between the wind velocity and the current velocity. Figure 10 is the stability diagram of a single-point- moored shuttle tanker, which verifies that a relatively short bow-hawser suppresses the unstable motion of SPM system.
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From page 354...
... Figure 11: Stability diagram for TANDEM system as function of mooring stiffness and turret location 0 02 0.4 06 0.8 1 12 14 hawser length (IIL) Figure 10: Stability diagram for SPM system wind shows such a trend to stabilize the system because the selected model in OCIMF data has a deckhouse at stern, which induces a positive restoring moment.
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From page 355...
... As a result it is found that a nonlinear stability analysis predicts the occurrence of the limit cycle in terms of the Hopf bifurcation, but the quantities of the limit cycle such as motion amplitude cannot be obtained. In this section, we derived simplified nonlinear equations of motion for the tandem offloading system in order to understand the fishtailing phenomena.
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From page 356...
... The stability diagram of the tandem offloading system is quite different from those of a single point moored shuttle tanker and a turret moored FPSO. In the case of the tandem offloading system, the hawser length does not affect the stability significantly and the turret mooring may worsen the stability depending on its stiffness.
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From page 357...
... Did you find any noticeable difference in the simulation results when you included the memory effect comparing to low frequency equation model neglecting the memory effect? And, have you check numerically KramerKronig relation in very low frequency region where radiation damping is actually zero?
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From page 358...
... Do the authors include them in the simulations or the stability analysis? Are the mean wave drift forces, which are autonomous, included?
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From page 359...
... Since slowly varying wave drift forces are nonautonomous, it is difficult to include them in the stability analysis, as discussers pointed out. In this paper, drift forces were considered only in numerical simulations.
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Key Terms

  • stability analysis
  • hawser length
  • wave drift
  • stability diagram
  • shuttle tanker

  • drift forces
  • velocity ratio
  • mooring stiffness
  • damping force
  • limit cycle

  • turret mooring
  • static stability
  • slowly varying
  • nonlinear stability
  • unstable region

  • relative motion
  • shuttle tankers
  • hawser tension
  • memory effect
  • radiation damping

  • simplified nonlinear
  • moored vessels
  • nonlinear dynamics
  • varying wave
  • offshore mechanics

  • yaw motions
  • stiffness matrix
  • nonlinear equations
  • hopf bifurcation
  • low frequency


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