Dynamic Response Of Agravity Platform Under Random Wave Forces

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

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Random Wave Forces on a Vertical Cylinder in the Free Surface Zone at High Reynolds Numbers

Breaking Waves ◽

10.1007/978-3-642-84847-6_34 ◽

1992 ◽

pp. 305-310

Author(s):

Gert Klopman ◽

Jan K. Kostense

Keyword(s):

Free Surface ◽

Vertical Cylinder ◽

Reynolds Numbers ◽

Random Wave ◽

Wave Forces ◽

Surface Zone ◽

High Reynolds Numbers ◽

High Reynolds

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Seismic Analysis of a Double-Hinged Articulated Offshore Tower

Volume 1: Offshore Technology ◽

10.1115/omae2008-57672 ◽

2008 ◽

Author(s):

Syed Danish Hasan ◽

Nazrul Islam ◽

Khalid Moin

Keyword(s):

Seismic Analysis ◽

Offshore Structures ◽

Random Wave ◽

Wave Forces ◽

Offshore Structure ◽

Concentrated Mass ◽

Energy Principle ◽

Rotational Angle ◽

Sea Bed ◽

Time Histories

The response of offshore structures under seismic excitation in deep water conditions is an extremely complex phenomenon. Under such harsh environmental conditions, special offshore structures called articulated structures are feasible owing to reduced structural weight. Whereas, conventional offshore structure requires huge physical dimensions to meet the desired strength and stability criteria, therefore, are uneconomical. Articulated offshore towers are among the compliant offshore structures. These structures consist of a ballast chamber near the bottom hinge and a buoyancy chamber just below the mean sea level, imparting controlled movement against the environmental loads (wave, currents, and wind/earthquake). The present study deals with the seismic compliance of a double-hinged articulated offshore tower to three real earthquakes by solving the governing equations of motion in time domain using Newmark’s-β technique. For this purpose Elcentro 1940, Taft 1952 and Northridge 1994 earthquake time histories are considered. The tower is modeled as an upright flexible pendulum supported to the sea-bed by a mass-less rotational spring of zero stiffness while the top of it rigidly supports a deck in the air (a concentrated mass above water level). The computation of seismic and hydrodynamic loads are performed by dividing the tower into finite elements with masses lumped at the nodes. The earthquake response is carried out by random vibration analysis, in which, seismic excitations are assumed to be a broadband stationary process. Effects of horizontal ground motions are considered in the present study. Monte Carlo simulation technique is used to model long crested random wave forces. Effect of sea-bed shaking on hydrodynamic modeling is considered. The dynamic equation of motion is formulated using Lagrangian approach, which is based on energy principle. Nonlinearities due to variable submergence and buoyancy, added mass associated with the geometrical non-linearities of the system are considered. The results are expressed in the form of time-histories and PSDFs of deck displacement, rotational angle, base and hinge shear, and the bending moment. The outcome of the response establishes that seismic sea environment is an important design consideration for successful performance of hinges, particularly, if these structures are situated in seismically active zones of the world’s ocean.

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An Analytical Procedure to Predict Transverse Vibration Response of Jack-Up Riser under the Random Wave Load

Shock and Vibration ◽

10.1155/2020/5072989 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Fengde Wang ◽

Wensheng Xiao ◽

Yanan Yao ◽

Qi Liu ◽

Changjiang Li

Keyword(s):

Dynamic Response ◽

Oil And Gas ◽

Beam Theory ◽

Random Wave ◽

Wave Load ◽

Main Component ◽

Gas Leaks ◽

Jack Up ◽

Euler Bernoulli Beam ◽

Transverse Response

Marine riser is a key equipment in offshore drilling operation, and failure of the riser can lead to drilling moratorium; in severe cases, it may cause oil and gas leaks. In this paper, the time-dependent boundary conditions of the riser and the randomness of wave load are considered to improve the calculation efficiency and accuracy of the dynamic response of the jack-up riser. Based on the Euler–Bernoulli beam theory, an analytical method to determine the response of the jack-up riser subjected to the random wave load was established by the Mindlin–Goodman method in the frequency domain, and an experiment was carried out to verify it. The research shows that transverse dynamic response is the main component of the transverse response of the riser, and the method proposed is feasible to calculate the transverse response of the riser.

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Dynamic Response Analysis of a Spar Platform Subjected to Wind and Wave Forces

Volume 1: Offshore Technology ◽

10.1115/omae2008-57227 ◽

2008 ◽

Author(s):

Bernt J. Leira ◽

Dag Myrhaug ◽

Jarle Voll

Keyword(s):

Dynamic Response ◽

Roughness Parameter ◽

Response Analysis ◽

Wave Forces ◽

Wind Gust ◽

Wave Age ◽

Spar Platform ◽

Dynamic Response Analysis ◽

Wind Speeds ◽

Wind Response

Results from a study on dynamic response analysis of a floating production unit (FPSO) excited by wave and wind forces are presented. The FPSO is examplified by a Spar platform considering the motion in surge and pitch. The wind gust is modelled with the Harris [4] and Ochi and Shin [7] wind gust spectra. The effect of the wave age on the wind gust spectrum is included by adopting the Volkov wave age dependent sea surface roughness parameter [10]; the wave age independent Charnock roughness parameter [2] is also used as a reference. Examples of results demonstrate clear effects of wave age on the dynamic response. Moreover, for high mean wind speeds the total wind response is much smaller than the wave response, but for low mean wind speeds the wind appears to be more important.

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Probability distribution of random wave forces in weakly nonlinear random waves

Ocean Engineering ◽

10.1016/s0029-8018(99)00067-0 ◽

2000 ◽

Vol 27 (12) ◽

pp. 1391-1405 ◽

Cited By ~ 5

Author(s):

Jin-Bao Song ◽

Yong-Hong Wu ◽

B. Wiwatanapataphee

Keyword(s):

Probability Distribution ◽

Random Wave ◽

Wave Forces ◽

Random Waves ◽

Weakly Nonlinear ◽

Nonlinear Random Waves

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Prediction of the Damping-Controlled Response of Offshore Structures to Random Wave Excitation

Society of Petroleum Engineers Journal ◽

10.2118/7828-pa ◽

1980 ◽

Vol 20 (01) ◽

pp. 5-14 ◽

Cited By ~ 2

Author(s):

Kim J. Vandiver

Keyword(s):

Wave Spectrum ◽

Wave Force ◽

Ocean Waves ◽

Radiation Damping ◽

Explicit Calculation ◽

Random Wave ◽

Wave Forces ◽

Linear Wave ◽

Radiation Wave ◽

Diffraction Effects

Abstract A method is presented for predicting the damping-controlled response of a structure at a known natural frequency to random wave forces. The principal advantage of the proposed method over those in current use proposed method over those in current use is that explicit calculation of wave forces is not required in the analysis. This is accomplished by application of the principle of reciprocity: that the linear wave force spectrum for a particular vibration mode is proportional to the radiation (wave-making) proportional to the radiation (wave-making) damping of that mode. Several example calculations are presented including the prediction of the heave response of a prediction of the heave response of a tension-leg platform. The directional distribution of the wave spectrum included in the analysis. Introduction This paper introduces a simple procedure for estimating the dynamic response of a structure at each of its natural frequencies to the random excitation of ocean waves. The principal advantage of the proposed method is that the explicit calculation of wave forces has been eliminated from the analysis. This is made possible by a direct applications of the reciprocity relations for ocean waves, originally established by Haskind and described by Newman, in a form that is easy to implement. Briefly stated, fore many structures it is possible to derive a simple expression for the wave force spectrum in terms of the radiation damping and the prescribed wave amplitude spectrum. In general, such a substitution is of little use because the radiation damping coefficient may be equally difficult to find. However, the substitution leads to a very useful result when the dynamically amplified response at a natural frequency is of concern. In such cases it is shown that, contrary to popular belief, the response is not inversely proportional to the total damping but is, in fact, proportional to the ratio of the radiation damping to the total damping. Therefore, in the absence of a reliable estimate of either the total damping or the ratio of the radiation component to the total, an upper bound estimate of the response still may be achieved because of the existence of this upper bound is one of the key contributions of this paper.Linear wave theory is assumed; therefore, excitation caused by drag forces is not considered. However, for many structures drag excitation is negligible except for very large wave events. In the design process extreme events are modeled deterministically process extreme events are modeled deterministically by means of a prescribed design wave and not stochastically as is done here. In many circumstances linear wave forces will dominate, and the results shown here will be applicable. Although drag-exciting forces are not included, damping resulting from hydrodynamic drag is included. Wave diffraction effects are extremely difficult to calculate. This analysis includes diffraction effects but never requires explicit evaluation of them.It has been recognized that directional spreading of the wave spectrum is an important consideration in the estimation of dynamic response. In this paper such effects are accounted for in closed-form expressions. The evaluation of the expressions requires knowledge of estimates of the variation of the modal exciting force with wave incidence angle. However, only the relative variation of the modal exciting force as a percent of that at an arbitrarily chosen reference angle is required. Evaluation of the wave force in absolute terms still is not required. SPEJ p. 5

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Random Wave Forces Near Free Surface

Journal of Waterway Port Coastal and Ocean Engineering ◽

10.1061/(asce)0733-950x(1990)116:2(232) ◽

1990 ◽

Vol 116 (2) ◽

pp. 232-251 ◽

Cited By ~ 9

Author(s):

Michael Isaacson ◽

John Baldwin

Keyword(s):

Free Surface ◽

Random Wave ◽

Wave Forces

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Nonlinear Dynamic Response of a Compliant Tower Under the Effect of Steady and Unsteady Sea States

Volume 3A: Structures, Safety and Reliability ◽

10.1115/omae2017-62449 ◽

2017 ◽

Cited By ~ 1

Author(s):

Konstantinos Chatziioannou ◽

Vanessa Katsardi ◽

Apostolos Koukouselis ◽

Euripidis Mistakidis

Keyword(s):

Structural Analysis ◽

Dynamic Response ◽

Deep Water ◽

Nonlinear Dynamic ◽

Wave Theory ◽

Random Wave ◽

Wave Loading ◽

Nonlinear Dynamic Response ◽

Steady Wave ◽

Compliant Tower

The purpose of this work is to highlight the importance of considering the actual nonlinear dynamic response for the analysis and design of fixed deep water platforms. The paper highlights the necessity of applying dynamic analysis through the comparison with the results obtained by the authors by applying static nonlinear analysis on the structure under examination. The example treated in the context of the present paper is a compliant tower, set-up in deep water. Nonlinearities are considered both for the calculation of the wave loadings and the structural analysis. The wave loading is based on linear random wave theory and comparisons are provided with the steady wave theories, Airy and Stokes 5th. The former solution is based on the most probable shape of a large linear wave on a given sea-state; the auto-correlation function of the underlying spectrum. On the other hand, in the field of structural analysis, two cases are considered for comparison, static analysis and time history dynamic analysis. For both types of analysis, two sub-cases are considered, a case in which geometric nonlinearity and nonlinearities related to the modelling of the soil are considered and a case in which the corresponding linear theories are employed (reference cases). The structural calculations were performed using the well-known structural analysis software SAP2000, which was enhanced by a special programming interface that was developed to calculate the wave loading and to directly apply the generated loads on the structural members. The results show that the consideration of the particle velocities associated with the linear random wave theory in the wave loading lead to significant differences with respect to the steady wave theories in terms of the displacements and stresses of the structure. Moreover, irrespectively of the adopted wave theory, the nonlinear analyses lead to significant discrepancies with respect to the linear ones. This is mainly associated with the nonlinear properties of the soil. Another source of discrepancies between the results of static and dynamic analyses stems from the change of the effective natural frequency of the structure when nonlinearities are considered.

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