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.

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]

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.

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.

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.

Comparative Assessment of Hydrodynamic Models in Slow-Motion Mooring Dynamics

1999 ◽  
Vol 122 (2) ◽  
pp. 109-117 ◽  
Author(s):  
Joa˜o Paulo J. Matsuura ◽  
Kazuo Nishimoto ◽  
Michael M. Bernitsas ◽  
Luis O. Garza-Rios
Keyword(s):  
Parametric Design ◽  
Slow Motion ◽  
Qualitative Behavior ◽  
Nonlinear Stability Analysis ◽  
Hydrodynamic Models ◽  
Steady Current ◽  
Mooring Dynamics ◽  
Ship Hydrodynamic ◽  
Quantitative Properties ◽  
Short Wing

The slow-motion dynamics of a turret mooring system is analyzed and compared for four of the most commonly used ship hydrodynamic maneuvering models. Each of those utilizes a different approach to model and then to calculate or measure the hydrodynamic forces and moment acting on the vessel. The four hydrodynamic maneuvering models are studied first by a physics-based analysis of each model and then by numerically comparing their prediction of equilibria, nonlinear stability analysis, bifurcation sequences, and morphogeneses of turret mooring systems. Catastrophe sets are constructed in two-dimensional parametric design spaces to determine the qualitative behavior of the system, and nonlinear time simulations are used to assess its quantitative properties. Static bifurcations of the principal equilibrium are compared to determine the nature of alternate equilibria. A turret-moored tanker is modeled with anchored catenaries, including nonlinear drag. External excitation is time independent, and for the numerical applications it is limited to steady current. Of the four models used, the Abkowitz and Takashina models show similar qualitative dynamics. The Obokata and Short-Wing models are also qualitatively similar, but very different from the first group. Limited sensitivity analysis pinpoints the source of discrepancy between the two schools of thought. [S0892-7219(00)01401-1]

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.

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.

Dynamic Analysis for the Design of CALM System in Shallow and Deep Waters

1997 ◽  
Vol 119 (3) ◽  
pp. 151-157 ◽  
Author(s):  
Y.-L. Hwang
Keyword(s):  
Mathematical Model ◽  
Dynamic Analysis ◽  
Model Test ◽  
Time Domain ◽  
Time Domain Analysis ◽  
Mooring Lines ◽  
Deep Waters ◽  
Wave Drift ◽  
The Mathematical Model ◽  
Survival Condition

This paper presents a time domain analysis approach to evaluate the dynamic behavior of the catenary anchor leg mooring (CALM) system under the maximum operational condition when a tanker is moored to the terminal, and in the survival condition when the terminal is not occupied by a tanker. An analytical model, integrating tanker, hawser, buoy, and mooring lines, is developed to dynamically predict the extreme mooring loads and buoy orbital motions, when responding to the effect of wind, current, wave frequency, and wave drift response. Numerical results describing the dynamic behaviors of the CALM system in both shallow and deepwater situations are presented and discussed. The importance of the line dynamics and hawser coupled buoy-tanker dynamics is demonstrated by comparing the present dynamic analysis with catenary calculation approach. Results of the analysis are compared with model test data to validate the mathematical model presented.

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