Motions of Articulated Towers and Moored Floating Structures

1989 ◽  
Vol 111 (3) ◽  
pp. 233-241 ◽  
Author(s):  
S. K. Chakrabarti ◽  
D. C. Cotter
Keyword(s):  
Degrees Of Freedom ◽  
Single Point ◽  
Body Motion ◽  
Single Frequency ◽  
Integration Scheme ◽  
Floating Structure ◽  
Mooring Lines ◽  
Random Seas ◽  
Exciting Forces ◽  
The Time Domain

A versatile and efficient method of analysis has been developed to analyze a mooring system composed of a floating structure, e.g., a ship, mooring lines, fenders, and an articulated tower. The floating structure is assumed to be large, but may have an arbitrary shape, and the tower is assumed to be axisymmetrical. Although the program treats the floating structure and tower as a system, each body may be examined alone in the absence of the other. The analysis is carried out in the time domain assuming rigid body motion, and the solution is generated by a forward integration scheme. This approach permits nonlinear line and fender forces to be incorporated readily into the analysis. The exciting forces in the analysis are wind, current, and waves, which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. The vessel is free to respond to the exciting forces in six degrees of freedom—surge, heave, sway, roll, pitch, and yaw. The tower is free to respond in two degrees of freedom—oscillation and precession. The analysis has been extensively verified with several different model tests for different structure configurations in regular and random seas. These include an articulated tower, a single-point mooring tanker system, a floating caisson and an inclined mooring tower.

Numerical Simulation of Multiple Floating Structures With Nonlinear Constraints

2002 ◽  
Vol 124 (2) ◽  
pp. 104-109 ◽  
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Degrees Of Freedom ◽  
Order Theory ◽  
Frequency Domain Analysis ◽  
Body Motion ◽  
Single Frequency ◽  
Integration Scheme ◽  
Mooring Lines ◽  
Floating Structures ◽  
Irregular Wave ◽  
Exciting Forces

A versatile and efficient numerical analysis is developed to compute the responses of a moored floating system composed of multiple floating structures. Structures such as tankers, semisubmersibles, FPSOs, SPARs, TLPs, and SPMs connected by mooring lines, connectors or fenders may be analyzed individually or collectively including multiple interaction. The analysis is carried out in the time domain assuming rigid body motion for the structures, and the solution is generated by a forward integration scheme. The analysis includes the nonlinearities in the excitation, damping, and restoring terms encountered in a typical mooring system configuration. It also allows for instabilities in the tower oscillation as well as slack mooring lines. Certain simplifications in the analysis have been made, which are discussed. The exciting forces in the analysis are wind, current, and waves (including a steady and an oscillating drift force), which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. For regular waves either linear, stretched linear or fifth order theory may be used. The irregular wave may be included as a given spectral model (e.g., PM or JONSWAP). The vessels are free to respond to the exciting forces in six degrees of freedom—surge, sway, heave, roll, pitch, and yaw. The tower, when present, is free to respond in two degrees of freedom—oscillation and precession. The loads in the mooring lines are determined from prescribed tension-strain tables for the lines. Rigid mooring arms can be analyzed by allowing for compression in the load-strain table. Fenders may be input similarly through load compression tables. In order to establish the stability and accuracy of the solution, comparison of the results with linearized frequency domain analysis was made. The analysis is verified by several different model test results for different structure configurations in regular and random seas. Some of the interesting aspects of nonlinear system are shown with a few examples.

Semi-Submersible Floater’s VIM Simulation Method for Mooring Line Safety Assessment

2018 ◽  
Author(s):  
Toshifumi Fujiwara
Keyword(s):  
Safety Assessment ◽  
Simulation Method ◽  
Oscillator Model ◽  
Design Stage ◽  
Mooring Line ◽  
Floating Structure ◽  
Mooring Lines ◽  
Wake Oscillator Model ◽  
Wake Oscillator ◽  
The Time Domain

The author proposed the Vortex-induced Motion (VIM) simulation method of a semi-submersible type offshore floating structure using the wake oscillator model based on the potential theory and model test data. This method is easy to use for the time-domain simulation of the VIM amplitude, that is in-line, transverse and yaw motions, of the semi-submersible floater in case of being demented mooring safety assessment of that. The simulation method presented in this paper was modified the single circular floater simulation method with the wake oscillator model for a semi-submersible floater. Some empirical parameters, obtained from the systematic model tests used many semi-submersible floaters, are only decided from external form of the semi-submersible floaters, that is the column / lower hull ratio etc. This simulation method is able to indicate general VIM trend and to be used for the assessment of mooring lines safety in the design stage. Using the VIM amplitude simulation, fatigue damage of mooring lines on one sample semi-submersible floater was investigated as an example.

A Numerical Method for Representing Retardation Functions With Complex Exponentials

2017 ◽  
Author(s):  
Fushun Liu ◽  
Lei Jin ◽  
Jiefeng Chen ◽  
Wei Li
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Memory Effects ◽  
Floating Structure ◽  
Frequency Dependent ◽  
Laplace Domain ◽  
The Time Domain ◽  
Frequency Domain Techniques

Numerical time- or frequency-domain techniques can be used to analyze motion responses of a floating structure in waves. Time-domain simulations of a linear transient or nonlinear system usually involve a convolution terms and are computationally demanding, and frequency-domain models are usually limited to steady-state responses. Recent research efforts have focused on improving model efficiency by approximating and replacing the convolution term in the time domain simulation. Contrary to existed techniques, this paper will utilize and extend a more novel method to the frequency response estimation of floating structures. This approach represents the convolution terms, which are associated with fluid memory effects, with a series of poles and corresponding residues in Laplace domain, based on the estimated frequency-dependent added mass and damping of the structure. The advantage of this approach is that the frequency-dependent motion equations in the time domain can then be transformed into Laplace domain without requiring Laplace-domain expressions of the added mass and damping. Two examples are employed to investigate the approach: The first is an analytical added mass and damping, which satisfies all the properties of convolution terms in time and frequency domains simultaneously. This demonstrates the accuracy of the new form of the retardation functions; secondly, a numerical six degrees of freedom model is employed to study its application to estimate the response of a floating structure. The key conclusions are: (1) the proposed pole-residue form can be used to consider the fluid memory effects; and (2) responses are in good agreement with traditional frequency-domain techniques.

A Comparison of Time Domain and Frequency Domain Approaches for the Fully Coupled Analysis of Deepwater Floating Systems

2006 ◽  
Author(s):  
Ying Min Low ◽  
Robin S. Langley
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Coupled Analysis ◽  
Integration Scheme ◽  
Global Coordinate System ◽  
Mooring Lines ◽  
Frequency Domain Methods ◽  
The Time Domain ◽  
Fully Coupled ◽  
Fully Coupled Analysis

The recognition of the need for a fully coupled analysis of deepwater floating production systems has led to the research and development of several coupled analysis tools in recent years. Barring a handful of exceptions, these tools and available commercial packages are invariably in the time domain. This has resulted in a much better understanding and confidence in time domain coupled analysis, but less so for the frequency domain approach. In this paper, the viability of frequency domain coupled analysis is explored by performing a systematic comparison of time and frequency domain methods using computer programs developed in-house. In both methods, a global coordinate system is employed where the vessel is modeled with six degrees-of-freedom, while the mooring lines and risers are discretized as lumped masses connected by extensional and rotational springs. Coupling between the vessel and the mooring lines is achieved by stiff springs, and the influence of inertia and damping from the lines are directly accounted for without the need for prior assumptions. First and second order wave forces generated from a random environment are applied on the vessel, as well as drag and inertia loading on the lines. For the time domain simulation, the Wilson-theta implicit integration scheme is employed to permit the use of relatively large time steps. The frequency domain analysis is highly efficient despite being formulated in global coordinates, owing to the banded characteristics of the mass, damping and stiffness matrices. The nonlinear drag forces are stochastically linearized iteratively. As both the time and frequency domain models of the coupled system are identical, a consistent assessment of the error induced by stochastic linearization can be made.

scholarly journals Water Entry of A Wedge Into Waves in Three Degrees Offreedom

2019 ◽  
Vol 26 (1) ◽  
pp. 117-124
Author(s):  
Shi Yan Sun ◽  
Hai Long Chen ◽  
Gang Xu
Keyword(s):  
Degrees Of Freedom ◽  
Mutual Effect ◽  
Vertical Direction ◽  
Physical Space ◽  
Auxiliary Function ◽  
Body Motion ◽  
Wave Loading ◽  
Initial Stage ◽  
The Time Domain ◽  
Three Degrees Of Freedom

Abstract The hydrodynamic problem of a two-dimensional wedge entering into a nonlinear wave in three degrees of freedom is investigated based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. To avoid numerical difficulties due to an extremely small contact area at the initial stage, a stretched coordinate system is used based on the ratio of the Cartesian system in the physical space to the distance travelled by the wedge in the vertical direction. The mutual dependence of body motion and wave loading is decoupled by using the auxiliary function method. Detailed results about body accelerations, velocities and displacements at different Froude numbers or different waves are provided, and the mutual effect between body motion and wave loading is analysed in depth.

scholarly journals Mooring Drag Effects in Interaction Problems of Waves and Moored Underwater Floating Structures

2020 ◽  
Vol 8 (3) ◽  
pp. 146
Author(s):  
Cheng-Tsung Chen ◽  
Jaw-Fang Lee ◽  
Chun-Han Lo
Keyword(s):  
Water Waves ◽  
Degrees Of Freedom ◽  
Wave Force ◽  
Wave Forces ◽  
Linear Potential ◽  
Floating Structure ◽  
Mooring Lines ◽  
Wave Fields ◽  
Present Solution ◽  
Scattering And Radiation

In contrast to either considering structures with full degrees of freedom but with wave force on mooring lines neglected or with wave scattering and radiation neglected, in this paper, a new analytic solution is presented for wave interaction with moored structures of full degrees of freedom and with wave forces acting on mooring lines considered. The linear potential wave theory is applied to solve the wave problem. The wave fields are expressed as superposition of scattering and radiation waves. Wave forces acting on the mooring lines are calculated using the Morison equation with relative motions. A coupling formulation among water waves, underwater floating structure, and mooring lines are presented. The principle of energy conservation, as well as numerical results, are used to verify the present solution. With complete considerations of interactions among waves and moored structures, the characteristics of motions of the structure, the wave fields, and the wave forces acting on the mooring lines are investigated.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

Experimental Investigation vs Numerical Simulation of the Dynamic Response of a Moored Floating Structure to Waves

2014 ◽  
Author(s):  
Daniele Dessi ◽  
Sara Siniscalchi Minna
Keyword(s):  
Dynamical Behavior ◽  
Irregular Waves ◽  
Mooring Line ◽  
Floating Structure ◽  
Mooring Lines ◽  
Wave Energy Converters ◽  
Time Histories ◽  
Actual Configuration ◽  
Proper Orthogonal ◽  
Dynamic Wave

A combined numerical/theoretical investigation of a moored floating structure response to incoming waves is presented. The floating structure consists of three bodies, equipped with fenders, joined by elastic cables. The system is also moored to the seabed with eight mooring lines. This corresponds to an actual configuration of a floating structure used as a multipurpose platform for hosting wind-turbines, aquaculture farms or wave-energy converters. The dynamic wave response is investigated with numerical simulations in regular and irregular waves, showing a good agreement with experiments in terms of time histories of pitch, heave and surge motions as well as of the mooring line forces. To highlight the dynamical behavior of this complex configuration, the proper orthogonal decomposition is used for extracting the principal modes by which the moored structure oscillates in waves giving further insights about the way waves excites the structure.

Optimized Mooring Line Simulation Using a Hybrid Method Time Domain Scheme

2014 ◽  
Author(s):  
Niels Hørbye Christiansen ◽  
Per Erlend Torbergsen Voie ◽  
Jan Høgsberg ◽  
Nils Sødahl
Keyword(s):  
Hybrid Method ◽  
Time Domain ◽  
Computation Time ◽  
Mooring Line ◽  
Mooring Lines ◽  
Fem Model ◽  
Input Variables ◽  
The Time Domain ◽  
The Cost ◽  
Short Time

Dynamic analyses of slender marine structures are computationally expensive. Recently it has been shown how a hybrid method which combines FEM models and artificial neural networks (ANN) can be used to reduce the computation time spend on the time domain simulations associated with fatigue analysis of mooring lines by two orders of magnitude. The present study shows how an ANN trained to perform nonlinear dynamic response simulation can be optimized using a method known as optimal brain damage (OBD) and thereby be used to rank the importance of all analysis input. Both the training and the optimization of the ANN are based on one short time domain simulation sequence generated by a FEM model of the structure. This means that it is possible to evaluate the importance of input parameters based on this single simulation only. The method is tested on a numerical model of mooring lines on a floating off-shore installation. It is shown that it is possible to estimate the cost of ignoring one or more input variables in an analysis.

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