A comparative study of the first and second order theories and Goda's formula for wave-induced pressure on a vertical breakwater with irregular waves

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.

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

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4001415 ◽

2010 ◽

Vol 132 (4) ◽

Cited By ~ 1

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.

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WAVE LOADS ON HORIZONTAL CYLINDERS

Coastal Engineering Proceedings ◽

10.9753/icce.v16.147 ◽

1978 ◽

Vol 1 (16) ◽

pp. 147

Author(s):

P. Holmes ◽

J.R. Chaplin

Keyword(s):

Oscillatory Flow ◽

Vertical Plane ◽

Vertical Cylinder ◽

Irregular Waves ◽

Wave Loads ◽

Incident Flow ◽

Cylinder Axis ◽

Straight Line ◽

Horizontal Cylinders ◽

Wave Induced

The problem of predicting wave induced loads on cylinders is an enormously complex one. It is clear from the scatter present in most experimental determinations of force coefficients that there are many individual factors which influence the mechanisms of flow induced loading. Among these are some, for instance Reynolds number, separation and periodic vortex shedding, which are inter-related and whose influences cannot be studied in isolation. Others, such as shear flow, irregular waves and free surface effects, can at least be eliminated in the laboratory, in order to approach an understanding of the more fundamental characteristics of the flow. A vertical cylinder in uniform waves experiences an incident flow field which can be described in terms of rotating velocity and acceleration vectors, always in the same vertical plane, containing also the cylinder axis, whose magnitudes are functions of time and of position along the length of the cylinder. Some of the essential features of this flow can be studied under two-dimensional oscillatory conditions, in which either the cylinder or the fluid is oscillated relative to the other along a straight line (planar oscillatory flow). The incident velocity and acceleration vectors are then always concurrent, normal to the cylinder axis, and oscillating in magnitude with time.

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A comparative study of the second-order Born and Faddeev-Watson approximations. II. Charge transfer

Journal of Physics B Atomic and Molecular Physics ◽

10.1088/0022-3700/20/3/017 ◽

1987 ◽

Vol 20 (3) ◽

pp. 551-564 ◽

Cited By ~ 10

Author(s):

M J Roberts

Keyword(s):

Charge Transfer ◽

Comparative Study ◽

Second Order

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Bending Moments and Shear Forces in Ships Sailing in Irregular Waves

Journal of Ship Research ◽

10.5957/jsr.1981.25.4.243 ◽

1981 ◽

Vol 25 (04) ◽

pp. 243-251

Author(s):

J. Juncher Jensen ◽

P. Terndrup Pedersen

Keyword(s):

Linear Part ◽

Vertical Motion ◽

Bending Moment ◽

Irregular Waves ◽

Bending Moments ◽

Shear Forces ◽

Strip Theory ◽

Wave Heights ◽

Exciting Forces ◽

Wave Induced

This paper presents some results concerning the vertical response of two different ships sailing in regular and irregular waves. One ship is a containership with a relatively small block coefficient and with some bow flare while the other ship is a tanker with a large block coefficient. The wave-induced loads are calculated using a second-order strip theory, derived by a perturbational procedure in which the linear part is identical to the usual strip theory. The additional quadratic terms are determined by taking into account the nonlinearities of the exiting waves, the nonvertical sides of the ship, and, finally, the variations of the hydrodynamic forces during the vertical motion of the ship. The flexibility of the hull is also taken into account. The numerical results show that for the containership a substantial increase in bending moments and shear forces is caused by the quadratic terms. The results also show that for both ships the effect of the hull flexibility (springing) is a fair increase of the variance of the wave-induced midship bending moment. For the tanker the springing is due mainly to exciting forces which are linear with respect to wave heights whereas for the containership the nonlinear exciting forces are of importance.

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Nonlinear Wave Disturbance Around a Vertical Circular Column

21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 1 ◽

10.1115/omae2002-28620 ◽

2002 ◽

Cited By ~ 1

Author(s):

C. T. Stansberg ◽

H. Braaten

Keyword(s):

Linear Prediction ◽

Harmonic Component ◽

Nonlinear Effects ◽

Second Order ◽

Wave Disturbance ◽

Difference Frequency ◽

Irregular Waves ◽

Order Effects ◽

Sum Frequency ◽

Circular Column

The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m, in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum-frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required.

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Influence of Multidirectional Irregular Wave Sampling to Second-Order Hydroelastic Responses of VLFS

Volume 4: Ocean Engineering; Ocean Renewable Energy; Ocean Space Utilization, Parts A and B ◽

10.1115/omae2009-79861 ◽

2009 ◽

Author(s):

Xujun Chen ◽

Torgeir Moan ◽

Xuefeng Tang

Keyword(s):

Computer Time ◽

Second Order ◽

Irregular Waves ◽

Floating Structure ◽

First Order ◽

Fluid Forces ◽

Irregular Wave ◽

Very Large Floating Structure ◽

Principal Coordinates ◽

Hydroelastic Response

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 this theory, four types of multidirectional irregular wave samplings are introduced, the frequency steps Δω of the four samplings are 0.04, 0.04, 0.02 and 0.01 rad/s, and the corresponding numbers of wave components N are 17, 75, 147 and 285 respectively. The result of principal coordinates and displacements of a very large floating structure (VLFS) for the four types of sampling are presented and discussed. The influence of the sampling is analyzed. The conclusions show that the sampling of the multidirectional irregular waves influence the second-order hydroelastic response of the VLFS. The accuracy and the computer time of the calculating with sampling of frequency step Δω = 0.02 rad/s are acceptable.

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Extreme Response Predictions for Jack-Up Units in Second Order Stochastic Waves by FORM

Volume 2: Structures, Safety and Reliability; Petroleum Technology Symposium ◽

10.1115/omae2007-29022 ◽

2007 ◽

Cited By ~ 2

Author(s):

Jo̸rgen Juncher Jensen

Keyword(s):

Second Order ◽

Sea State ◽

First Order ◽

Reliability Method ◽

Extreme Response ◽

Stochastic Waves ◽

Short Time ◽

Wave Induced ◽

Jack Up ◽

Operational Time

The aim of the present paper is to advocate for a very effective stochastic procedure, based on the First Order Reliability Method (FORM), for extreme value predictions related to wave induced loads. All kinds of non-linearities can be included, as the procedure makes use of short time-domain simulations of the response in question. The procedure will be illustrated with a jack-up rig where second order stochastic waves are included in the analysis. The result is the probability of overturning as function of sea state and operational time.

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