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]

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.

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.

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.

Electrokinetic Flow Instability in High Concentration Gradient Microflows

2002 ◽  
Author(s):  
Chuan-Hua Chen ◽  
Juan G. Santiago
Keyword(s):  
Wave Speed ◽  
Flow Instability ◽  
Ionic Concentration ◽  
Qualitative Behavior ◽  
Common Channel ◽  
High Concentration ◽  
Electrokinetic Flow ◽  
Quantitative Properties ◽  
Material Line ◽  
Ongoing Project

This paper documents the scalar imaging of an electrokinetic flow instability that is directly relevant to microfluidic systems that aim to handle and analyze heterogeneous sample streams. The instability occurs in simple T-junctions where two streams of different ionic concentration flow into a common channel. Using neutral dye visualizations, general qualitative behavior of the instability is documented including the formation of a wave in the stream/stream material line that originates at the junction of the two channels and propagates downstream. Several quantitative properties of this phenomenon are measured including wave speed and the extent of the perturbation boundary. This work is part of an ongoing project to identify the physics of this instability and determine the regime of stability, with an ultimate goal of developing methods to either enhance or suppress the instability.

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.

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.

Stability-Based Design of Two-Point Mooring Systems With Hydrodynamic Memory

1997 ◽  
Vol 119 (1) ◽  
pp. 61-69
Author(s):  
J.-S. Chung
Keyword(s):  
Stability Analysis ◽  
Bifurcation Diagram ◽  
Memory Effect ◽  
Nonlinear Stability ◽  
Slow Motion ◽  
Mooring Line ◽  
Nonlinear Stability Analysis ◽  
Tension Level ◽  
Design Variables ◽  
Parameter Values

A systematic method of determining the design parameter values of two-point mooring (TPM) systems is presented. The conclusions of nonlinear stability analysis of horizontal plane slow motion dynamics of TPM systems with hydrodynamic memory are used to guide selection of the design variables. Specifically, within the stable regions of bifurcation diagram, a set of parameter values is chosen systematically to examine the corresponding TPM system. Then, each TPM system is simulated and the results are evaluated in terms of given criteria such as tension level of the mooring line or offset of the moored vessel. The hydrodynamic memory effect due to the oscillatory motions of moored vessel is included in the formulation. The memory effect influences the stability properties of TPM systems and alters the design chart/bifurcation diagram and particularly the static loss and dynamic loss of stability. The significance of hydrodynamic memory on several TPM systems is illustrated by comparing the statistics of the simulations. The design approach implemented in this work shows that nonlinear stability theory can be used effectively in the actual design process of mooring systems to reduce dramatically the number of simulations required. It is also shown that the often inconclusive nonlinear time simulations can be guided by theoretical nonlinear stability analysis of system dynamics to produce improved design values of system parameters of TPM systems.

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 Model reduction of the tippedisk: a path to the full analysis

2021 ◽  
Author(s):  
Simon Sailer ◽  
Remco I. Leine
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Full Detail ◽  
Qualitative Behavior ◽  
Nonlinear Stability Analysis ◽  
Full System ◽  
Reduced Equations ◽  
Highly Nonlinear ◽  
System Equations ◽  
Inversion Phenomenon

AbstractThe tippedisk is a mechanical-mathematical archetype for friction-induced instability phenomena that exhibits an interesting inversion phenomenon when spun rapidly. The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. The qualitative behavior of the nonlinear system can be analyzed, leading to slow–fast dynamics. Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. In a first step the full system equations are linearized around the inverted spinning solution with the aim to obtain a local stability analysis. However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. The reduced equations are presented here in full detail and are compared numerically with the full model. Furthermore, using the reduced equations we give approximate closed form results for the critical spinning speed of the tippedisk.

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