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.

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.

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.

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.

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.

scholarly journals Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yingguo Li
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Recurrent Neural Network ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Nonlinear Dynamical ◽  
Bifurcation Direction ◽  
The Stability ◽  
Manifold Theory

We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.

scholarly journals Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Chuandong Li ◽  
Wenfeng Hu ◽  
Tingwen Huang
Keyword(s):  
Hopf Bifurcation ◽  
Epidemic Model ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Normal Form Theory ◽  
Computer Viruses ◽  
Stability And Bifurcation ◽  
Form Theory ◽  
The Stability

We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.

Achieve of Torpedo Shell Parameter Model Based on Secondary Development of UG

2012 ◽  
Vol 542-543 ◽  
pp. 532-536
Author(s):  
Nan Li ◽  
Yun Peng Zhao
Keyword(s):  
Design Process ◽  
Parametric Design ◽  
Three Dimensional ◽  
Secondary Development ◽  
Design Parameters ◽  
Three Dimensional Model ◽  
Three Dimensional Modeling ◽  
Modeling Software ◽  
Shell Parameter ◽  
Set Up

Torpedo shell Modeling is a very important part in the design process. However, the traditional method of torpedo shell modeling is only the GUI of CAD drawing software. If there is change in individual parameters, designers have to start again from scratch. Such method will waste of resources. This paper set up the torpedo shell parametric design process with secondary development language UG / Open API, and user-oriented menu creation tool UG / Open UIStyler of UG,which is a three-dimensional modeling software, So that designers can be directly obtained three-dimensional model of the torpedo shell needing to enter the necessary design parameters. Meanwhile the designers can save design resources, and it helps optimize the latter part of the torpedo shell design.

Hydrodynamic Memory Effect on Stability, Bifurcation, and Chaos of Two-Point Mooring Systems

1997 ◽  
Vol 41 (01) ◽  
pp. 26-44
Author(s):  
Jin-Sug Chung ◽  
Michael M. Bernitsas
Keyword(s):  
Memory Effect ◽  
Design Parameters ◽  
Wave Loads ◽  
Mooring Lines ◽  
Stability Boundaries ◽  
The Stability ◽  
Systems With Memory ◽  
Hydrodynamic Wave ◽  
Nonlinear Elastic ◽  
With Memory

The stability properties of two-point mooring systems governed by their slow horizontal motions are studied theoretically. The often-neglected memory effect due to hydrodynamic wave loads change—in some cases critically—the stability boundaries in the system design space. The third-order maneuvering equations and a nonlinear elastic spring model are used to describe the dynamics of the moored vessel and the mooring lines, respectively. The resulting model accurately represents a two-point mooring system and can be used for stability analysis in the sense of Lyapunov. The stability charts of mooring systems with memory effects exhibit considerable differences from systems without memory in local regions of bifurcation diagrams. Further, the pattern of these changes of stability boundaries varies with the hydrodynamic properties of the moored vessel and/or the environmental conditions. The findings of this study suggest that the number of influencing design parameters can be much more than the present stability theory of dynamical systems can handle. They prove, however, that neglecting the memory effect may result in selecting unsafe configurations of two-point mooring systems.

Influence of optimally amplified streamwise streaks on the Kelvin–Helmholtz instability

2018 ◽  
Vol 838 ◽  
pp. 478-500 ◽  
Author(s):  
Mathieu Marant ◽  
Carlo Cossu
Keyword(s):  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Basic Flow ◽  
Sensitivity Analyses ◽  
Mean Flow ◽  
Helmholtz Instability ◽  
Flow Distortion ◽  
Streamwise Streaks ◽  
The Stability

The optimal energy amplifications of streamwise-uniform and spanwise-periodic perturbations of the hyperbolic-tangent mixing layer are computed and found to be very large, with maximum amplifications increasing with the Reynolds number and with the spanwise wavelength of the perturbations. The optimal initial conditions are streamwise vortices and the most amplified structures are streamwise streaks with sinuous symmetry in the cross-stream plane. The leading suboptimal perturbations have opposite (varicose) symmetry. When forced with finite amplitudes these perturbations modify the characteristics of the Kelvin–Helmholtz instability. Maximum temporal growth rates are reduced by optimal sinuous perturbations and are slightly increased by varicose suboptimal ones. In contrast, the onset of absolute instability is delayed by varicose suboptimal perturbations and is slightly promoted by sinuous optimal ones. We show that if, instead of the computed fully nonlinear basic-flow distortions, the stability analysis is based on a shape assumption for the flow distortions, then opposite effects on the flow stability are predicted in most of the considered cases. These strong differences are attributed to the spanwise-uniform component of the nonlinear basic-flow distortion which, we conclude, should be systematically included in sensitivity analyses of the stability of two-dimensional basic flows to three-dimensional basic-flow perturbations. We finally show that the leading-order quadratic sensitivity of the eigenvalues to the amplitude of the streaks is preserved if the effects of the mean flow distortion are included in the sensitivity analysis.

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