Low-Frequency Phenomena Associated With Vessels Moored at Sea

1975 ◽  
Vol 15 (06) ◽  
pp. 487-494 ◽  
Author(s):  
J.A. Pinkster
Keyword(s):  
Wave Height ◽  
Low Frequency ◽  
Second Order ◽  
Irregular Waves ◽  
Ship Motions ◽  
Wave Forces ◽  
Mooring System ◽  
Frequency Wave ◽  
First Order ◽  
The Mean

Abstract The influence of the low-frequency-wave-drifting force on the motions of moored vessels and the loads in the mooring system is demonstrated from results of model tests in irregular waves. The origin of the wave drifting force is discussed and methods for calculating the mean drifting force are reviewed. To facilitate calculation of the low-frequency-wave drifting force on an object in irregular waves, an existing method using the mean drifting force in regular waves is generalized. The results of calculations using the method introduced in this paper are compared with previously published test results. Finally, some remarks are added concerning effects that have not been accounted for in existing calculation methods. Introduction A vessel moored at sea in stationary conditions with regard to waves, wind, and current is subjected to forces that tend to shift it from the desired position. For a given vessel and position in the position. For a given vessel and position in the horizontal plane, the motions depend on both the mooring system and the external forces acting on the vessel. In steady conditions, the forces caused by a constant wind and current are constant quantities for a given heading angle of the vessel. The forces caused by a stationary irregular sea are of an irregular nature and may be split into two parts: first-order oscillatory forces with wave parts: first-order oscillatory forces with wave frequency, and second-order, slowly varying forces with frequencies much lower than the wave frequency.The first-order oscillatory wave forces on a vessel cause the well known ship motions whose frequencies equal the frequencies present in the spectrum of the irregular waves. These are the linear motions of surge, sway, and heave and the three angular motions of roll, pitch, and yaw. In general, the first-order wave forces are proportional to the wave height, as are the ensuing motions. The magnitude of the linear oscillatory motions is in the order of the height of the waves.The second-order wave forces, perhaps better known as the wave drifting forces, have been shown to be proportional to the square of the wave height. These forces, though small in magnitude, are the cause of the low-frequency, large-amplitude, horizontal motions sometimes observed in large vessels moored in irregular waves. Tests run in irregular waves in wave tanks of the Netherlands Ship Model Basin revealed a number of properties and effects of the low-frequency-wave properties and effects of the low-frequency-wave drifting force that are discussed here using the results of two test programs.The first of these programs concerns tests run with the model of a 125,000-cu m LNG carrier moored in head seas with an ideal linear mooring system. The second program deals with a 300,000-DWT VLCC moored with a realistic nonlinear bow hawser to a single-buoy mooring in waves, wind, and current coming from different directions.The results of the tests with the LNG carrier are shown in Figs. 1 through 3, while the results of the tests with the 300,000-DWT VLCC are shown in Fig. 4. All results are given in full-scale values. Fig. 1 shows the wave trace and the surge motion of the LNG carrier to a base of time. SPEJ P. 487

Mean- and Low-Frequency Wave Forces on Semisubmersibles

1982 ◽  
Vol 22 (04) ◽  
pp. 563-572
Author(s):  
J.A. Pinkster
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Forces ◽  
Frequency Wave ◽  
First Order ◽  
Wave Drift ◽  
Frequency Components ◽  
Wave Drift Forces ◽  
Drift Forces

Abstract Mean- and low-frequency wave drift forces on moored structures are important with respect to low-frequency motions and peak mooring loads. This paper addresses prediction of these forces on semisubmersible-type structures by use of computations based on three-dimensional (3D) potential theory. The discussion includes a computational method based on direct integration of pressure on the wetted part of the hull of arbitrarily shaped structures. Results of computations of horizontal drift forces on a six-column semisubmersible are compared with model tests in regular and irregular waves. The mean vertical drift forces on a submerged horizontal cylinder obtained from model tests also are compared with results of computations. On the basis of these comparisons, we conclude that wave drift forces on semisubmersible-type structures in conditions of waves without current can be predicted with reasonable accuracy by means of computations based on potential theory. Introduction Stationary vessels floating or submerged in irregular waves are subjected to large first-order wave forces and moments that are linearly proportional to the wave height and that contain the same frequencies as the waves. They also are subjected to small second-order mean- and low- frequency wave forces and moments that are proportional to the square of the wave height. Frequencies of second-order low-frequency components are associated with the frequencies of wave groups occurring in irregular waves.First-order wave forces and moments cause the well-known first-order motions with wave frequencies. First-order wave forces and motions have been investigated for several decades. As a result of these investigations, methods have been developed to predict these forces and moments with reasonable accuracy for many different vessel shapes.For semisubmersibles, which consist of a number of relatively slender elements such as columns, floaters, and bracings, computation methods have been developed to determine the hydrodynamic loads on those elements without accounting for interaction effects between the elements. For the first-order wave loads and motion problem, these computations give accurate results.This paper deals with the mean- and low-frequency second-order wave forces acting on stationary vessels in regular and irregular waves in general and presents a method to predict these forces on the basis of computations.The importance of mean- and low-frequency wave drift forces, from the point of view of motion behavior and mooring loads on vessels moored at point of view of motion behavior and mooring loads on vessels moored at sea, has been recognized only within the last few years. Verhagen and Van Sluijs, Hsu and Blenkarn, and Remery and Hermans showed that the low-frequency components of wave drift forces in irregular waves-even though relatively small in magnitude-can excite large-amplitude low- frequency horizontal motions in moored structures. It was shown for irregular waves that the drift forces contain components with frequencies coinciding with the natural frequencies of the horizontal motions of moored vessels. Combined with minimal damping of low-frequency horizontal motions of moored structures, this leads to large-amplitude resonant behavior of the motions (Fig. 1). Remery and Hermans established that low-frequency components in drift forces are associated with the frequencies of wave groups present in an irregular wave train.The vertical components of the second-order forces sometimes are called suction forces. SPEJ p. 563

Accuracy Effects of Low Frequency Wave Loads on Ships Offshore to LNG Marine Terminal Design

2004 ◽  
Author(s):  
Monica J. Holboke ◽  
Robert G. Grant
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
Surface Boundary ◽  
Wave Loads ◽  
Wave Load ◽  
Frequency Wave ◽  
First Order ◽  
Terminal Design

This paper presents the results of a two-body analysis for a moored ship sheltered by a breakwater in shallow water with and without free surface forcing in the low frequency wave load calculation. The low frequency wave loads are determined by second order interactions from the first order. The free surface forcing term arises from the free surface boundary condition, which is trivial to first order but is not at second order. We demonstrate in the frequency domain the importance of this term in a two-body analysis. Additionally, we show how inaccurate calculations of the off-diagonal terms of the Quadratic Transfer Function can translate to over or under prediction of low frequency wave loads on moored ships sheltered by breakwaters in shallow water. Low frequency wave load accuracy has direct consequence for LNG marine terminal design. Generally, LNG marine terminals are sited in sheltered harbors, however increasingly they are being proposed in offshore locations where they will require protection from persistent waves and swells. Since breakwaters typically cost twice as much as the rest of the marine facilities, it is important to optimize their size, orientation and location. In a previous paper we described this optimization process [1], which identified a key step to be the transforming of waves just offshore the breakwater into wave loads on the moored ships. The ability to do this step accurately is of critical importance because if the loads are too large, the breakwater will be larger and more expensive than necessary and if the loads are too small, the terminal will experience excessive downtime and loss of revenue.

Second-Order Low-Frequency Wave Forces on a SPM Offloading Tanker in Shallow Water

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
S. Ma ◽  
M. H. Kim ◽  
S. Shi
Keyword(s):  
Shallow Water ◽  
Transfer Functions ◽  
Low Frequency ◽  
Wave Force ◽  
Second Order ◽  
Irregular Waves ◽  
Mooring Line ◽  
Frequency Wave ◽  
Water Region ◽  
Shallow Water Region

This paper studies the influence of three different calculation methods of the second-order low-frequency (LF) wave-force quadratic transfer functions (QTFs) for a single point mooring (SPM) tanker system in relatively shallow water region. The multivessel-mooring hawser coupled dynamic analysis is used to simulate the floater relative motions and mooring and hawser tensions. Because the SPM tanker is deployed in shallow water region and the slowly varying drift motions are to be dominant in typical operational conditions, the accurate calculation of LF wave-force QTFs become important especially for mooring and hawser-tension prediction. The practically popular Newman’s approximation and another approximation excluding complicated free-surface integrals are used to calculate the LF QTFs on the offloading tanker and they are compared with the complete QTF results. Further comparison is carried out by calculating the resulting LF wave-force spectra and motion time histories and analyzing their impacts on hawser and mooring line tensions. Through the example studies, the limitation of the Newman’s approximation in the case of shallow water and longer period irregular waves is underscored.

Second-Order Low-Frequency Wave Forces on a SPM Offloading Tanker in Shallow Water

2008 ◽  
Author(s):  
S. Ma ◽  
S. Shi ◽  
M. H. Kim
Keyword(s):  
Shallow Water ◽  
Transfer Functions ◽  
Low Frequency ◽  
Wave Force ◽  
Second Order ◽  
Dynamic Responses ◽  
Mooring Line ◽  
Wave Forces ◽  
Frequency Wave ◽  
The Impact

This paper studies the influence of three different calculation methods of the second-order low-frequency (LF) wave forces on the tanker responses and hawser/mooring tensions in relatively shallow water region. The vessel-mooring-riser coupled dynamic analysis computer program HARP is used to simulate the coupled dynamic responses of offloading tanker moored to a SPM (Single Point Mooring). Because the SPM is supposed to be deployed in shallow water and the slowly varying drift motions of the tanker are to dominate the motion responses in typical operational conditions, the accurate calculation of LF wave-force quadratic transfer functions (QTFs) becomes important especially for mooring and hawser tensions. Like common practice, the so-called Newman’s approximation and another approximation method without including complicated free-surface integrals are first used to calculate the LF QTFs on the offloading tanker and they are compared with the complete QTF results. Further comparison is performed by calculating the resulting LF wave-force spectra and response time series by using the three different methods. The impact of the three different approaches on vessel surge motions and hawser/mooring line tensions is also addressed.

scholarly journals Diffraction Measurements and Equilibrium Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Victor A. Sipachev
Keyword(s):  
Low Frequency ◽  
Mean Square ◽  
Structural Studies ◽  
Free Rotation ◽  
Theory Analysis ◽  
First Order ◽  
Internuclear Distances ◽  
The Mean ◽  
Asymmetry Parameters ◽  
First Order Perturbation

Structural studies are largely performed without taking into account vibrational effects or with incorrectly taking them into account. The paper presents a first-order perturbation theory analysis of the problem. It is shown that vibrational effects introduce errors on the order of 0.02 Å or larger (sometimes, up to 0.1-0.2 Å) into the results of diffraction measurements. Methods for calculating the mean rotational constants, mean-square vibrational amplitudes, vibrational corrections to internuclear distances, and asymmetry parameters are described. Problems related to low-frequency motions, including torsional motions that transform into free rotation at low excitation levels, are discussed. The algorithms described are implemented in the program available from the author (free).

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

2016 ◽  
Vol 60 (03) ◽  
pp. 145-155
Author(s):  
Ya-zhen Du ◽  
Wen-hua Wang ◽  
Lin-lin Wang ◽  
Yu-xin Yao ◽  
Hao Gao ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Linear Response Theory ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Loads ◽  
Floating Bodies ◽  
Drift Motion ◽  
First Order ◽  
Series Of Experiments ◽  
Deck Wetness

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

Extreme Response of Very Large Floating Structure Considering Second-Order Hydroelastic Effects in Multidirectional Irregular Waves

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Xujun Chen ◽  
Torgeir Moan ◽  
Shixiao Fu
Keyword(s):  
Second Order ◽  
Irregular Waves ◽  
Bending Moments ◽  
Floating Structure ◽  
First Order ◽  
Fluid Forces ◽  
Principal Coordinates ◽  
Vertical Displacements ◽  
Exciting Forces ◽  
Nonlinear Fluid

Hydroelasticity theory, considering the second-order fluid forces induced by the coupling of first-order wave potentials, is introduced briefly in this paper. Based on the numerical results of second-order principal coordinates induced by the difference-frequency and sum-frequency fluid forces in multidirectional irregular waves, the bending moments, as well as the vertical displacements of a floating plate used as a numerical example are obtained in an efficient manner. As the phase angle components of the multidirectional waves are random variables, the principal coordinates, the vertical displacements, and the bending moments are all random variables. Extreme values of bending moments are predicted on the basis of the theory of stationary stochastic processes. The predicted linear and nonlinear results of bending moments show that the influences of nonlinear fluid forces are different not only for the different wave phase angles, but also for the different incident wave angles. In the example very large floating structure (VLFS) considered in this paper, the influence of nonlinear fluid force on the predicted extreme bending moment may be as large as 22% of the linear wave exciting forces. For an elastic body with large rigidity, the influence of nonlinear fluid force on the responses may be larger than the first-order exciting forces and should be considered in the hydroelastic analysis.

Numerical Study on Hydrodynamic Responses of a Two-Body System in Side-by-Side Operation

2016 ◽  
Author(s):  
Shaowu Ou ◽  
Shixiao Fu ◽  
Wei Wei ◽  
Tao Peng ◽  
Xuefeng Wang
Keyword(s):  
Numerical Study ◽  
Low Frequency ◽  
Optimal Operation ◽  
Hydrodynamic Interactions ◽  
Irregular Waves ◽  
Mooring System ◽  
Time Varying ◽  
Body System ◽  
The Time Domain ◽  
Two Bodies

Typically, in some side-by-side offshore operations, the speed of vessels is very low or even 0 and the headings are manually maneuvered. In this paper, the hydrodynamic responses of a two-body system in such operations under irregular seas are investigated. The numerical model includes two identical PSVs (Platform Supply Vessel) as well as the fenders and connection lines between them. A horizontal mooring system constraining the low frequency motions is set on one of the ships to simulate maneuver system. Accounting for the hydrodynamic interactions between two bodies, 3D potential theory is applied for the analysis of their hydrodynamic coefficients. With wind and current effects included, these coefficients are further applied in the time domain simulations in irregular waves. The relevant coefficients are estimated by experiential formulas. Time-varying loads on fenders and connection lines are analyzed. Meanwhile, the relative motions as well as the effects of the hydrodynamic interactions between ships are further discussed, and finally an optimal operation scheme in which operation can be safely performed is summarized.

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

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