Random Wave Forces Research Articles

Time domain analysis of random wave forces on pipelines in the inertia regime

An experimental investigation on random wave induced forces on a smooth submarine pipeline, fixed horizontally near a plane boundary, is carried out in the inertia-dominated regime. The water particle kinematics at the centre line of the pipe are generated using linear numerical filters, derived from the time history of water surface elevation. The pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) at various energy levels to achieve different significant wave conditions. The in-line hydrodynamic coefficient of inertia and the transverse hydrodynamic coefficients of lift and vertical inertia are evaluated utilizing the measured forces and through the use of least-squares method in the time domain. These hydrodynamic coefficient are found to be a function of gap ration of the pipeline from the plane boundary and correlate very well with the potential flow results within the range of the Keulegan-Carpenter number or period parameter investigated.

Nonlinear surge response of a tension leg platform to random wave forces

The response of a Tension Leg Platform (TLP) to wave-induced forces depends upon different factors which are considered in the analysis. It is not possible to include all factors in one single analysis. As a result the relative importance of the factors needs to be evaluated by parametric studies. In the present paper, effects of some factors on the surge response of a TLP to random wave forces are investigated. The factors include (i) the variable submergence effects such as variation in added mass and tension fluctuation in the tethers, (ii) variation in tension in the tethers produced by vertical wave forces, and (iii) method for calculating hydrodynamic forces. The effect of variable submergence on the water particle kinematics is included by both Chakrabarti's 1 and Hogben's 2 approaches. Hydrodynamic forces on the large-diameter members of the superstructure are obtained by means of a modified Morison equation by using (a) average water-particle kinematics across the diameter of the members, (b) water-particle kinematics calculated at the centre of the cross section, and (c) water-particle kinematics the same as (b) above, but with the inertia coefficient modified to take into account any diffraction effect. The nonlinear equation of motion describing the surge motion of the TLP is solved in the time domain by using an iterative step-by-step integration procedure.

Forces on Vertical Cylinder Due to Random Waves

Random wave forces consisting of drag and inertia components are analyzed. The forces were measured in a wave tank experiment with circular cylinders at low Keulegan‐Carpenter numbers. The values of the hydrodynamic coefficients were chosen from the corresponding tests in regular waves. The method used in choosing these values applicable to the case of random waves is discussed. The nonlinear drag force contribution is linearized so that the spectral approach may be applied directly. Good correlations between the measured force spectra and the computed spectra were obtained in several cases of random waves. The short‐term distribution of the in‐line and transverse forces is shown. It is found that the in‐line force amplitudes follow the Rayleigh distribution reasonably well. The relations of the transverse force to an exponential distribution are exhibited.

Root mean square force coefficients for submarine pipelines

An experimental investigation has been carried out on forces induced by regular and random waves on submarine pipelines placed near a plane boundary. The inline and transverse forces are analysed in terms of combined root mean square (rms) hydrodynamic coefficient. The total rms coefficient is correlated with Keulegan-Carpenter number or period parameter and relative clearance of the pipeline from the plane boundary. The pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) in the random wave force tests. The time histories of water particle kinematics are generated using the linear numerical transforms. This paper also reports the effect of depth parameter on the total rms coefficient. The results of the random wave force tests are finally compared with those of regular waves.

Dynamic response analysis of soil-offshore structure systems

Dynamic soil-structure interaction seems to have significant roles in the response evaluation of the dynamic response analysis of offshore structures subjected to wave forces. The emphasis is placed upon the evaluation of the dynamic interaction of a soil-structure interaction system due to random wave forces which are represented with a power spectral density function of the Bretschneider type. The governing equation of the soil-offshore structure system is formulated with the substructure method. Consequently, it is shown that the dynamic soil-structure interaction plays important roles in the evaluation of the dynamic responses for the offshore structure system. The response due to the dynamic soil-structure interaction provides larger evaluations than the rigidly supported base conditions. The first few modes' evaluations appear to have significant contributions to the response of the dynamic soil-structure interaction system.

Decomposition of wave forces into linear and non-linear components

This paper details a methodology for analyzing non-linear systems involving a square-law operation with sign. The analysis is applied specifically to the problem of decomposing random wave forces on an ocean structure into their inertial (linear) and drag (non-linear) components. A procedure is presented for identifying the individual inertial and drag force parameters based solely upon measurements of the input wave velocity and the output wave force, where the wave velocity has an arbitrary spectral density function and mean value, and the inertial and drag forces have an arbitrary frequency dependence and phase. It is assumed only that the wave velocity is a Gaussian random process. Experimental verifications of the analysis procedure are presented.

Adaptive Prediction of the Motion of Marine Vehicles

A predictor of the future motion of a vessel subject to random wave and wind forces, would have a variety of applications in ocean engineering. Most previous work has assumed that the wave spectrum is known and that the vessel is modeled accurately; both factors affect the predictor performance strongly. In practice, the relevant data is difficult to measure on a manoeuvering vessel and can change significantly with operating conditions. Here were describe the application of an adaptive algorithm which predicts the future of a signal from its history. The predictor adapts to the signal and varies its parameters to optimise the prediction. Operating on a signal with a stationary spectrum, the predictor tends to a steady performance; if the spectrum changes, the predictor quickly adjusts to the new situation. We illustrate the performance of the system with examples.

Random dynamic analysis of multi-body offshore structures

A general method for the dynamic analysis of multi-body offshore structures is presented, being based on a constraint matrix approach. A method of deriving the constraint matrix for a general structure is given, and this is then used to derive the equations of motion of a whole system from those of it's component parts. The response of the system to both first and second order random wave forces is found and then used to calculate the forces and moments in the connecting mechanisms. The structure is assumed to have rigid component parts and a linearised frequency domain analysis method is used, although other methods are discussed. To illustrate it's use, the method is applied to both the SBS and Yoke-CALM design of offshore mooring terminal.

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

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 is that the 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) damping of that mode. Several example calculations are presented including the prediction of the heave response of a tension-leg platform. The directional distribution of the wave spectrum is included in the analysis.

Digital Simulation of Nonlinear Random Waves

Digital realizations of unidirectional nonlinear random seas correct to second order in an ocean of finite depth are simulated from three types of two-parameter theoretical spectra and are compared with measured hurricane-generated realizations by means of chi-square goodness-of-fit measures computed from the Gram-Charlier probability distribution in which the statistical measures of skewness and the excess of kurtosis are determined from the measured hurricane-generated realizations. The finite Fourier transform (FFT) algorithm is shown to be an efficient method for nonlinear simulations since the FFT coefficients are complex and, therefore, capable of retaining the nonlinear random phase interactions. The second-order nonlinear simulations demonstrate improved third-order and fourth-order statistical moments compared to the linear Gaussian simulations. Previous comparisons with measured wave forces on cylindrical pilings have demonstrated improvements in the statistics of random wave force predictions computed by digital filter methods as a result of these improved nonlinear random sea simulations.

Detection of Structural Failure on Fixed Platforms By Measurement of Dynamic Response

THIS PRESENTATION IS SUBJECT TO CORRECTION Offshore Technology Conference on behalf of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. (Society of Mining Engineers, The Metallurgical Society and Society of Petroleum Engineers), American Association of Petroleum. Geologists, American Institute of Chemical Engineers, American Society of Civil Engineers, American Society of Mechanical Engineers, Institute of Electrical and Electronics Engineers, Marine Technology Society, Society of Exploration Geophysicists, and Society of Naval Architects and Marine Engineers. This paper was prepared for presentation at the Seventh Annual Offshore Technology Conference to be held in Houston, Tex., May 5–8, 1975. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. Such use of an abstract should contain conspicuous acknowledgment of where and by whom, the paper is presented. presented Abstract A technique is described that can be used to detect subsurface structural failure by detecting changes in the natural frequencies of the structure. The experimental techniques are discussed, as well as the parameters which determine the minimum detectable damage level. Statistical Energy Analysis is introduced as a method for predicting the dynamic response of a wide variety of fixed and floating offshore structures to random wave forces. Introduction As offshore platforms are erected in progressively deeper waters, the problem progressively deeper waters, the problem of on site inspection of subsurface structural members becomes increasingly difficult and expensive. The current use of divers is hampered by poor visibility, poor lighting and hazardous conditions. These obstacles worsen rapidly with increase in depth. In addition, marine growth and corrosion may conceal structural defects. The inadequacy of current inspection techniques is amplified by the frequent reports of total or near total loss of platforms. The inspection technique described here requires periodic measurement of selected natural frequencies that show direct response to wind and waves. Wind and wave force spectra are sufficiently broad band random excitation to drive most offshore structures at one or more of their natural frequencies. Accelerometers can be used to measure the platform response, and from the records the platform response, and from the records the natural frequencies can be determined. Such determinations might be made on a semiannual or annual basis. A detected shift in natural frequency between successive measurements would indicate a change in the mass or stiffness of the structure. A reduction in stiffness implies failure in the structural members and joints, or in the supporting bottom conditions. In some circumstances the measurements might be helpful in determining the location of the failure. At the very least the periodic inspection can be used as the "go" or "no go" decision maker for a much more expensive diver survey. A detailed study of one offshore pile supported tower was conducted. The pile supported tower was conducted. The tower is a welded steel space frame with four primary legs, braced with horizontal and diagonal members.

A Time Series Model for Dynamic Behavior of Offshore Structures

Abstract An analytical model is presented for evaluating the dynamic behavior of offshore structures subject to earthquake and storm wave forces. A mathematical model is formulated as a system of nonlinear differential equations that are solved by direct numerical integration on a digital computer. The offshore structure is represented in the model by a lumped mass system with linear stiffness and damping characteristics. Nonlinearities arise from the representation of hydrodynamic forces on the structure by the Morison equation, with velocities and accelerations based on the relative motion between structure and water. Random wave forces are obtained from wave velocities and accelerations simulated from a Pierson-Moskowitz wave spectrum. Earthquake Pierson-Moskowitz wave spectrum. Earthquake excitation consists of a time history of horizontal base accelerations obtained from actual or simulated earthquake accelerograms. Results are presented in the form of root mean square (rms) values, maximum amplitudes, and power spectra for nodal deflections and accelerations, base shear and overturning moment. Results from the analysis of four prototype structures in water depths of 400 to 1,000 ft showed: (1) dynamic response to waves is significant for structures with a fundamental natural period greater than approximately 2.4 seconds; (2) including relative water-structure motion in the Morison force equation contributes significantly to damping of structural vibration; and (3) the statistical nature of extreme values for structural response to waves is not adequately described by the commonly assumed Rayleigh distribution. Introduction Engineering practices for most offshore drilling platforms built to date have been based on static platforms built to date have been based on static analysis methods. Such methods provide adequate designs because the resulting structures are relatively stiff with fundamental periods of vibration below the range of significant wave energy. However, the recent interest and activity in deeper water development has emphasized the need for investigating the potential dynamic behavior of offshore structures. A number of analysis techniques are reported in the literature, most of which can be broadly classified as spectral, or frequency domain, methods. The results of some of these investigations have been reported. The model developed in this paper is based on a time domain approach, in which the dynamic behavior of an offshore structure subject to wave or earthquake forces is studied sequentially in time. The advantage of this approach is that nonlinear functional relationships, which require approximations in the spectral models, can be handled exactly. For example, the model includes an exact representation of the square-law, hydrodynamic drag force and the additional effect of relative water-structure motion in the drag force equation. The paper is presented in two parts. Part I presents the mathematical model of the structure in presents the mathematical model of the structure in waves and earthquakes and describes its implementation on a digital computer. Part II presents the results of analyses of four deepwater presents the results of analyses of four deepwater platforms to demonstrate the significance of dynamic platforms to demonstrate the significance of dynamic behavior and to show the importance of including structure motion in the hydrodynamic force equation.

Response of Offshore Structures to Random Wave Forces

Response of offshore structures to random wave action is presented. A theory for evaluating the response of these structures in deep water is described by the linear wave theory and the Gaussian processes. Hydrodynamic forces are computed through the Morrision-O’Brien-Britschneider formula. Some results of this application to several towers are given.

Directions de recherche du programme actions des éléments du comité d'études marines

The Institut Francais du Petrole has been running an overall study on the effects of wind, waves and currents on offshore drilling rigs since 1967, with the object of providing oil company engineers with better working methods. This is the first investigation of its kind ever to have been undertaken in France. The work put into this study was amply justified in view of the wide scope offered by oil prospection at sea, the need for more precise knowledge of environmental action and the importance of narrowing down the risk factor in the construction of new rigs. The programme is being carried out with direct participation of the Neptune undertaking and the assistance of Doris , IMF Lille, LNH Chatou, the Delft hydraulics laboratory and Franlab. It covers the following subjects : (i) Periodic Waves. Several models have been compared in the light of mathematical criteria and by considering the calculated forces acting on a pile in order to illustrate the resu!ts. The only really satisfactory form of wave representation is based on the stream function. (ii) Random waves, which are characterised by their energy spectrum. In this connection, models by Neumann, Breischneider-Scott-Pierson and Moscowitz will be compared with a view to establishing possible fields of application. (iii) The proccssing of recorded wave data and problems connected with it with a view to determining a wave spectrum (filtering) will be examined. (iv) Wave forces on structures can be calculated by the Morrison O'Brien formula. This is the only convenient method available for small bodies. No precise values are known for coefficients Cd and Cm; these should be expressed in terms of the wave velocity and acceleration field at a given point, which will also require experimental confirmation. A different approach will be required for larger bodies, for which wave diffraction should be taken into account. (i) Random wave forces can be estimated by Borgman's method, which will be applied to a fixed rig. (ii)By studying wind action, closer information can be obtained on the action and structure of gusts, static effects, resonance effects between rolling motion and gusts, and other similar phenomena. (iii) Available strength of materials programmes more specifically designed for petroleum engineering applications should be established ; for example, a study of vibrating structures should provide useful information. As an overall programme of this type should produce concrete results, experimental in situ measurements or on actual operational structures require particular care and attention.

Spectrum of Wave Drag on a Pile

SYNOPSISThe spectrum of random wave forces on a pile is derived by the method of characteristic function for a general case where waves are propagating on a current.It is demonstrated that the existence of a flow intensifies considerably the wave force.