Luis O. Garza-Rios

Effect of mooring line arrangement on the dynamics of spread mooring systems

A design methodology is formulated to reveal the dependence of nonlinear slow motion dynamics of Spread Mooring Systems (SMS) on mooring line arrangement. For a given SMS configuration, catastrophe sets are developed in the parametric design space showing the dependence of stability boundaries and singularities of bifurcations on design variables. This approach eliminates the need for nonlinear simulations. For general SMS design, however, the designer relies on experience rather than scientific understanding of SMS nonlinear dynamics, due to the high number of design variables. Several numerical applications are used to demonstrate counterintuitive ways of improving SMS dynamics. The SMS design methodology formulated in this paper aims at providing fundamental understanding of the effects of mooring line arrangement and pretension on SMS horizontal plane dynamics. Thus, the first guidelines are developed to reduce trial and error in SMS design. The methodology is illustrated by comparing catastrophe sets for various SMS configurations with up to three mooring lines. Numerous examples for a barge and a tanker SMS which exhibit qualitatively different nonlinear dynamic behaviour are provided.

Slow motion dynamics of turret mooring and its approximation as single point mooring

The mathematical model for the nonlinear dynamics of slow motions in the horizontal plane of Turret Mooring Systems (TMS) is presented. It is shown that the TMS model differs from the classical Single Point Mooring (SPM) model, which is used generally to study the TMS dynamics. The friction moment exerted between the turret and the vessel, and the mooring line damping moment resulting from the turret rotation are the sources of difference between TMS and SPM. Qualitative differences in the dynamical behavior between these two mooring systems are identified using nonlinear dynamics and bifurcation theory. In two- and three-dimensional parametric design spaces, the dependence of stability boundaries and singularities of bifurcations for given TMS and SPM configurations is revealed. It is shown that the static loss of stability of a TMS can be located approximately by the SPM static bifurcation. The dynamic loss of stability of TMS and the associated morphogenesis may be affected strongly by the friction/damping moment, and to a lesser extent, by the mooring line damping. Nonlinear time simulations are used to assess the effects of these properties on TMS and compared to SPM systems. The TMS mathematical model consists of the nonlinear horizontal plane fifth-order, large drift, low speed maneuvering equations. Mooring line behavior is modeled quasistatically by submerged catenaries, including nonlinear drag and touchdown. External excitation consists of time independent current, steady wind, and second-order mean drift forces.

Analytical expressions of the bifurcation boundaries for symmetric spread mooring systems

Abstract For a general symmetric Spread Mooring System .(SMS), the five necessary and sufficient conditions for stability are derived analytically. It is shown that only two conditions are dominant in symmetric ship moorings. The equations derived in this paper provide analytical means for determining static and dynamic loss of stability, as well as elementary singularities and roots to chaos, of symmetric SMS configurations, such as those recommended by the American Petroleum Institute. Thus, first it becomes easy to identify the morphogenesis occurring when a bifurcation boundary is crossed; and second, it is possible to determine the dependence of a symmetric SMS on any design parameter—such as mooring line length, orientation, pretension, etc. Theoretical results are verified by comparison to numerical results generated with nonlinear dynamics and codimension one and two bifurcation theory. The mathematical model of the SMS consists of the nonlinear third order manoeuvring equations without memory of the horizontal plane slow motion dynamics—surge, sway, and yaw—of a vessel moored to several terminals. Mooring lines are modeled as synthetic nylon ropes, chains, or steel cables. External excitation consists of time independent current, wind, and mean wave drift forces.

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

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

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.

Preliminary Design of Differentiated Compliance Anchoring Systems

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.

Numerical implementation and marine applications of an energy finite element formulation

The statistical energy analysis (SEA) is an established numerical technique appropriate to high‐frequency vibro‐acoustic analysis [R. Lyon, Statistical Energy Analysis of Dynamical Systems: Theory and Applications (MIT, Cambridge, MA, 1975)]. The energy finite element analysis (EFEA) constitutes a recent theoretical development [O. M. Bouthier and R. J. Bernhard, ‘‘Models of space averaged energetics of plates,’’ AIAA J. 30(3) (March 1992)]. In this work a numerical implementation of the EFEA is utilized for analyzing two marine structures, and numerical results are compared to SEA solutions from VAPEPS. First, a plate assembly representing the engine foundation of a frigate ship is analyzed. Previous SEA results and test date are available in the literature and they are included in the comparison [R. Lyon, ‘‘In‐plane contribution to structural noise transmission,’’ Noise Control Eng. J. 26, 22–27 (1986)]. In the second application the structure of a fishing boat is modeled by both methods. The results ar...

SLOW MOTION DYNAMICS OF DICAS MOORINGSYSTEMS UNDER STEADY CURRENT, WIND, ANDSTEADY DRIFT EXCITATION

The slow motion dynamical behavior of a Differentiated Compliance Anchoring System (DICAS), subject to a range of directions of external excitation of constant magnitude, located in the Marlin Field, Campos Basin, Brazil, is assessed based on nonlinear stability analysis and bifurcation theory. Excitation consists of steady current, wind, and second order mean wave drift forces. Catastrophe sets are constructed in a two-dimensional parametric design space, separating regions of qualitatively different dynamics. Stability analysis defines the morphogeneses occurring across bifurcation boundaries to find stable and limit cycle response near the principal equilibrium position. The resulting design graphs allow the designer to select an appropriate orientation and other design variables for DICAS without resorting to trial and error, or extensive nonlinear time simulations. The position of the vessel at equilibrium defines the mean horizontal displacement of the system with respect to a prescribed initial orientation. This position depends on the magnitude and direction of the external excitation. Limited simulations or further nonlinear analysis enable the designer to investigate whether or not DICAS slow motions comply with the allowable limits of motions for safe operations. The effect of water depth variation on the stability of DICAS is considered, and it is shown that the dynamics of the system change considerably with relatively small variation in water depth. The DICAS mathematical model consists of the nonlinear, horizontal plane fifth-order, large drift, low-speed maneuvering equations. Mooring lines are modeled by catenaries with touchdown and nonlinear drag. External excitation consists of time independent current, steady wind, and second order mean wave drift forces.