Mooring System Design Based on Analytical Expressions of Catastrophes of Slow-Motion Dynamics

1997 ◽  
Vol 119 (2) ◽  
pp. 86-95 ◽  
Author(s):  
M. M. Bernitsas ◽  
L. O. Garza-Rios
Keyword(s):  
Parametric Design ◽  
Sufficient Conditions ◽  
Slow Motion ◽  
Mooring System ◽  
Mooring Lines ◽  
Steel Cables ◽  
The Stability ◽  
Wave Drift Forces ◽  
Analytical Expressions ◽  
Motion Dynamics

Analytical expressions of the necessary and sufficient conditions for stability of mooring systems representing bifurcation boundaries, and expressions defining the morphogeneses occurring across boundaries are presented. These expressions provide means for evaluating the stability of a mooring system around an equilibrium position and constructing catastrophe sets in any parametric design space. These expressions allow the designer to select appropriate values for the mooring parameters without resorting to trial and error. A number of realistic applications are provided for barge and tanker mooring systems which exhibit qualitatively different nonlinear dynamics. The mathematical model consists of the nonlinear, third-order maneuvering equations of the horizontal plane slow-motion dynamics of a vessel moored to one or more terminals. Mooring lines are modeled by synthetic nylon ropes, chains, or steel cables. External excitation consists of time-independent current, wind, and mean wave drift forces. The analytical expressions presented in this paper apply to nylon ropes and current excitation. Expressions for other combinations of lines and excitation can be derived.

Analytical Expressions of the Stability and Bifurcation Boundaries for General Spread Mooring Systems

1996 ◽  
Vol 40 (04) ◽  
pp. 337-350
Author(s):  
Luis O. Garza-Rios ◽  
Michael M. Bernitsas
Keyword(s):  
Sufficient Conditions ◽  
Slow Motion ◽  
Mooring Lines ◽  
Codimension One ◽  
Dynamic Loss ◽  
Steel Cables ◽  
The Stability ◽  
Wave Drift Forces ◽  
System Configurations ◽  
Analytical Expressions

Spread mooring systems (SMS) are labeled as general when they are not restricted by conditions of symmetry. The six necessary and sufficient conditions for stability of general SMS are derived analytically. The boundaries where static and dynamic loss of stability occur also are derived in terms of the system eigenvalues, thus providing analytical means for defining the morphogenesis that occurs when a bifurcation boundary is crossed. The equations derived in this paper provide analytical expressions of elementary singularities and routes to chaos for general mooring system configurations. Catastrophe sets are generated first by the derived expressions and then numerically using nonlinear dynamics and codimension-one and -two bifurcation theory; agreement is excellent. The mathematical model consists of the nonlinear, third-order maneuvering equations without memory of the horizontal plane, slow-motion dynamics—surge, sway, and yaw—of a vessel moored to several terminals. Mooring lines can be modeled by synthetic nylon ropes, chains, or steel cables. External excitation consists of time-independent current, wind, and mean wave drift forces. The analytical expressions derived in this paper apply to nylon ropes and current excitation. Expressions for other combinations of lines and excitation can be derived.

Turret Mooring Design Based on Analytical Expressions of Catastrophes of Slow-Motion Dynamics

1998 ◽  
Vol 120 (3) ◽  
pp. 154-164 ◽  
Author(s):  
M. M. Bernitsas ◽  
L. O. Garza-Rios
Keyword(s):  
Parametric Design ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Slow Motion ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Mooring Lines ◽  
The Stability ◽  
Fifth Order ◽  
Analytical Expressions

Analytical expressions of the bifurcation boundaries exhibited by turret mooring systems (TMS), and expressions that define the morphogeneses occurring across boundaries are developed. These expressions provide the necessary means for evaluating the stability of a TMS around an equilibrium position, and constructing catastrophe sets in two or three-dimensional parametric design spaces. Sensitivity analyses of the bifurcation boundaries define the effect of any parameter or group of parameters on the dynamical behavior of the system. These expressions allow the designer to select appropriate values for TMS design parameters without resorting to trial and error. A four-line TMS is used to demonstrate this design methodology. The mathematical model consists of the nonlinear, fifth-order, low-speed, large-drift maneuvering equations. Mooring lines are modeled with submerged catenaries, and include nonlinear drag. External excitation consists of time-independent current, wind, and mean wave drift.

Analytical Expressions for Stability and Bifurcations of Turret Mooring Systems

1998 ◽  
Vol 42 (03) ◽  
pp. 216-232
Author(s):  
Luis O. Garza-Rios ◽  
Michael M. Bernitsas
Keyword(s):  
Parametric Design ◽  
Sufficient Conditions ◽  
Mooring Lines ◽  
Design Variables ◽  
Stability And Bifurcations ◽  
Dynamic Loss ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Fifth Order ◽  
Analytical Expressions

The eight necessary and sufficient conditions for stability of turret mooring systems (TMS) are derived analytically. Analytical expressions for TMS bifurcation boundaries where static and dynamic loss of stability occur are also derived. These analytical expressions provide physics-based means to evaluate the stability properties of TMS, find elementary singularities, and describe the morphogeneses occurring as a parameter (or design variable) or group of parameters are varied. They eliminate the need to compute numerically the TMS eigenvalues. Analytical results are verified by comparison to numerical results generated by direct computation of eigenvalues and their bifurcations. Catastrophe sets (design charts) are constructed in the two-dimensional parametric design space to show the dependence of design variables on the stability of the system. The TMS mathematical model consists of the nonlinear horizontal plane—surge, sway and yaw—fifth-order, large drift, low speed maneuvering equations. Mooring lines are modeled quasistatically by catenaries. External excitation consists of time independent current, steady wind, and second-order mean drift forces.

Effect of Slow-Drift Loads on Nonlinear Dynamics of Spread Mooring Systems

1998 ◽  
Vol 120 (4) ◽  
pp. 201-211 ◽  
Author(s):  
M. M. Bernitsas ◽  
B.-K. Kim
Keyword(s):  
Nonlinear Dynamics ◽  
Horizontal Plane ◽  
Parametric Design ◽  
Slow Motion ◽  
Third Order ◽  
Mooring Lines ◽  
Slow Drift ◽  
Restoring Forces ◽  
The Mathematical Model ◽  
Drift Forces

Spread mooring systems (SMS) may experience large-amplitude oscillations in the horizontal plane due to slow-drift loads. In the literature, this phenomenon is attributed to resonance. In this paper, it is shown that this conclusion is only partially correct. This phenomenon is investigated using nonlinear stability and bifurcation analyses which reveal an enhanced picture of the nonlinear dynamics of SMS. Catastrophe sets are developed in a parametric design space to define regions of qualitatively different system dynamics for autonomous SMS, including mean drift forces. Limited time simulations are performed to verify the qualitative conclusions drawn on the nonlinear dynamics of SMS using catastrophe sets. Slowly varying drift forces are studied as an additional excitation on the autonomous SMS and simulations reveal that slow drift may cause resonance or bifurcations with stabilizing or destabilizing morphogeneses. The mathematical model of SMS is based on the slow-motion maneuvering equations in the horizontal plane (surge, sway, yaw), including hydrodynamic forces with terms up to third-order, nonlinear restoring forces from mooring lines, and environmental loads due to current, wind, and wave-drift.

Dynamics of Spread Mooring Systems With Hybrid Mooring Lines

2000 ◽  
Vol 122 (4) ◽  
pp. 274-281 ◽  
Author(s):  
Luis O. Garza-Rios ◽  
Michael M. Bernitsas ◽  
Kazuo Nishimoto ◽  
Joa˜o Paulo J. Matsuura
Keyword(s):  
Stability Analysis ◽  
Deep Water ◽  
Parametric Design ◽  
Line Tension ◽  
Slow Motion ◽  
Synthetic Fiber ◽  
Mooring Line ◽  
Vertical Force ◽  
Mooring Lines ◽  
Steady Current

The weight of a chain mooring line in deep water is the main source of mooring line tension. Chain weight also induces a vertical force on the moored vessel. To achieve the desired tension without excessive weight, hybrid mooring lines, such as lighter synthetic fiber ropes with chains, have been proposed. In this paper, the University of Michigan methodology for design of mooring systems is developed to study hybrid line mooring. The effects of hybrid lines on the slow-motion nonlinear dynamics of spread mooring systems (SMS) are revealed. Stability analysis and bifurcation theory are used to determine the changes in SMS dynamics in deep water based on pretension and angle of inclination of the mooring lines for different water depths and synthetic rope materials. Catastrophe sets in two-dimensional parametric design spaces are developed from bifurcation boundaries, which delineate regions of qualitatively different dynamics. Stability analysis defines the morphogeneses occurring as bifurcation boundaries are crossed. The mathematical model of the moored vessel consists of the horizontal plane—surge, sway, and yaw—fifth-order, large drift angle, low-speed maneuvering equations. Mooring lines are modeled quasistatically as nonlinear elastic strings for synthetic ropes and as catenaries for chains, and include nonlinear drag and touchdown. Excitation consists of steady current, wind, and mean wave drift. Numerical applications are limited to steady current, which is adequate for revealing the SMS design depending on the selected parameters. [S0892-7219(00)00804-9]

Effect of Size and Position of Supporting Buoys on the Dynamics of Spread Mooring Systems

2000 ◽  
Vol 123 (2) ◽  
pp. 49-56 ◽  
Author(s):  
Luis O. Garza-Rios ◽  
Michael M. Bernitsas
Keyword(s):  
Stability Analysis ◽  
Deep Water ◽  
Parametric Design ◽  
Slow Motion ◽  
System Stability ◽  
Mooring Lines ◽  
Steady Current ◽  
Dynamic Loss ◽  
Fifth Order ◽  
The Mathematical Model

Vessels moored in deep water may require buoys to support part of the weight of the mooring lines. The effects that size and location of supporting buoys have on the dynamics of spread mooring systems (SMS) at different water depths are assessed by studying the slow motion nonlinear dynamics of the system. Stability analysis and bifurcation theory are used to determine the changes in SMS dynamics in deep water based as functions of buoy parameters. Catastrophe sets in a two-dimensional parametric design space are developed from bifurcation boundaries, which separate regions of qualitatively different dynamics. Stability analysis defines the morphogeneses occurring as bifurcation boundaries are crossed. The mathematical model of the moored vessel consists of the horizontal plane—surge, sway, and yaw—fifth-order, large-drift, low-speed maneuvering equations. Mooring lines made of chains are modeled quasi-statically as catenaries supported by buoys including nonlinear drag and touchdown. Steady excitation from current, wind, and mean wave drift are modeled. Numerical applications are limited to steady current and show that buoys affect both the static and dynamic loss of stability of the system, and may even cause chaotic response.

Effect of Memory on the Stability of Spread Mooring Systems

1999 ◽  
Vol 43 (03) ◽  
pp. 157-169
Author(s):  
Boo-Ki Kim ◽  
Michael M. Bernitsas
Keyword(s):  
System Dynamics ◽  
Memory Effect ◽  
Parametric Design ◽  
Slow Motion ◽  
Synthetic Fiber ◽  
Nonlinear Phenomena ◽  
Impulse Response Functions ◽  
Mooring Lines ◽  
Modeling And Analysis ◽  
Convolution Integrals

The importance of including the hydrodynamic memory effect in modeling and analysis of spread mooring systems (SMS) is assessed based on the design methodology for mooring systems developed at the University of Michigan. The memory effect is modeled by the hydrodynamic radiation forces expressed in terms of added mass at infinite frequency and convolution integrals of impulse response functions. The convolution integrals, which are explicit functions of time, are converted to autonomous excitation by the method of extended dynamics. For a given SMS configuration, nonlinear stability and bifurcation theory are used to produce catastrophe sets in the parametric design space separating regions of qualitatively different system dynamics. This approach reveals the complete picture of nonlinear phenomena associated with system dynamics and eliminates the need for extensive simulations. Catastrophe sets are developed in several parametric design spaces, providing fundamental understanding of the memory effects on SMS nonlinear dynamics. The mathematical model is based on the slow-motion maneuvering equations in the horizontal plane, including hydrodynamic memory effect and third-order quasi-steady hydrodynamic forces. Mooring lines are modeled by synthetic fiber ropes attached to surface terminals and deep-water catenary chains with touchdown and nonlinear drag. Environmental loads consist of time-independent current, wind, and mean wave drift forces.

Preliminary Design of Differentiated Compliance Anchoring Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 9-15 ◽  
Author(s):  
L. O. Garza-Rios ◽  
M. M. Bernitsas ◽  
K. Nishimoto ◽  
I. Q. Masetti
Keyword(s):  
Parametric Design ◽  
Dynamical Behavior ◽  
Open Water ◽  
Slow Motion ◽  
Preliminary Design ◽  
Mooring Lines ◽  
Campos Basin ◽  
Anchoring System ◽  
Fifth Order ◽  
The Mathematical Model

The preliminary design of a differentiated compliance anchoring system (DICAS) is assessed based on stability of its slow-motion nonlinear dynamics using bifurcation theory. The system is to be installed in the Campos Basin, Brazil, for a fixed water depth under predominant current directions. Catastrophe sets are constructed in a two-dimensional parametric design space, separating regions of qualitatively different dynamics. Stability analyses define the morphogeneses occurring across bifurcation boundaries to find stable and limit cycle dynamical behavior. These tools allow the designer to select appropriate values for the mooring parameters without resorting to trial and error, or extensive nonlinear time simulations. The vessel equilibrium and orientation, which are functions of the environmental excitation and their motion stability, define the location of the top of the production riser. This enables the designer to verify that the allowable limits of riser offset are satisfied. The mathematical model consists of the nonlinear, horizontal plane fifth-order large-drift, low-speed maneuvering equations. Mooring lines are modeled by open-water catenary chains with touchdown effects and include nonlinear drag. External excitation consists of time-independent current, wind, and mean wave drift.

scholarly journals Transient Responses Evaluation of FPSO with Different Failure Scenarios of Mooring Lines

2021 ◽  
Vol 9 (2) ◽  
pp. 103
Author(s):  
Dongsheng Qiao ◽  
Binbin Li ◽  
Jun Yan ◽  
Yu Qin ◽  
Haizhi Liang ◽  
...  
Keyword(s):  
Service Condition ◽  
Mooring Line ◽  
Mooring System ◽  
Transient Effects ◽  
Floating Platform ◽  
Transient Responses ◽  
Mooring Lines ◽  
Performance Deterioration ◽  
Steady State Responses ◽  
Influence Process

During the long-term service condition, the mooring line of the deep-water floating platform may fail due to various reasons, such as overloading caused by an accidental condition or performance deterioration. Therefore, the safety performance under the transient responses process should be evaluated in advance, during the design phase. A series of time-domain numerical simulations for evaluating the performance changes of a Floating Production Storage and Offloading (FPSO) with different broken modes of mooring lines was carried out. The broken conditions include the single mooring line or two mooring lines failure under ipsilateral, opposite, and adjacent sides. The resulting transient and following steady-state responses of the vessel and the mooring line tensions were analyzed, and the corresponding influence mechanism was investigated. The accidental failure of a single or two mooring lines changes the watch circle of the vessel and the tension redistribution of the remaining mooring lines. The results indicated that the failure of mooring lines mainly influences the responses of sway, surge, and yaw, and the change rule is closely related to the stiffness and symmetry of the mooring system. The simulation results could give a profound understanding of the transient-effects influence process of mooring line failure, and the suggestions are given to account for the transient effects in the design of the mooring system.

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