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In this study, an efficient time-domain prediction model is developed to predict unsteady flow vortex-induced vibrations (VIV) of flexible risers. The hydrodynamic forces on flexible risers are calculated on the basis of forced oscillation experiments on rigid cylinders. A period identification criterion, based on the spatial and temporal variations of reduced velocity, is proposed to divide the entire vibration process into exciting and damping periods of each exited mode. In exciting periods, assuming that VIV enters an ideal lock-in stage, a non-iterative solving model is established under modal space for response calculations, which efficiently predicts time domain VIV responses. In damping periods, free-decay vibration theory based recurrence formulas are established under modal space, and they get solved stepwise for modal responses. After some slight response adjustments to smooth period transitions, the VIV response time history can be obtained efficiently. This model is validated by steady flow VIV prediction cases, and further applied to predict oscillatory flow VIV experimental results. The prediction cases reveal that this model is able to realize high-speed VIV predictions with satisfactory results and no convergence problems. This model, with high efficiency and stability, is highly suitable for unsteady flow VIV prediction in engineering applications.

The Norwegian Public Road Administration is planning to upgrade Coastal Highway E39 by replacing ferry connections with floating bridges or submerged floating tunnels (SFTs). This study considers a potential pontoon-supported curved SFT designed for crossing Sognefjorden at a submergence of 12 m. It consists of two identical tubes with a diameter of 12.6 m each in a tandem configuration and with a length of approximately 4 km. The natural frequencies of the low-order modes are well within the energy content in the spectra of the second-order difference-frequency wave excitation forces and the vortex shedding-induced forces. In this paper, numerical simulation of wave-induced hydroelastic response and flow-induced vibrations of the twin-tube SFT is performed. Long- and short-crested waves, the first and second order wave loads, are considered. A time-domain approach to simulate crossflow vortex-induced vibration (VIV) and VIV-amplified inline drag forces, partly based on the coefficients obtained experimentally, is established and applied. The focus is on extreme conditions – relating to ultimate strength limit states. The second-order wave load substantially affects the lateral motion and lateral bending moment, as expected. The short-crested waves influence the response in both the lateral and vertical directions by exciting asymmetric eigenmodes. In strong flow conditions, once VIV is excited, the standard deviation of the vertical motion (of about 30% of the diameter) and the bending moment about the horizontal axis is more that an order of magnitude larger than that induced by the wave loads. The simulation of the wave- and flow-induced load effects provides a good reference for the design of SFTs.

In this paper, a time domain prediction method from experimental data is proposed for vortex-induced vibration (VIV) of flexible risers. The nonlinear factors, couplings among axial tension, VIV response in cross flow (CF) direction and the hydrodynamic force, have been taken into account in this method, with a simplified tension variation model and empirical hydrodynamic force model. The hydrodynamic force, including the excitation force in the excitation region and the damping force in the damping region are the function of excitation coefficients, non-dimensional VIV amplitude and frequency based on vibration experiment data. Iterations are performed to achieve balances between the hydrodynamic forces and the VIV responses of a riser. Moreover, a new added mass coefficient of 2.0 from model tests of flexible pipes is applied, where the predicted VIV response frequencies reveal higher accuracy. Comparison between the predicted results and the experimental results under uniform flow of 2.8 m/s and shear flow of 2.0 m/s are conducted, which verifies the feasibility and reliability of the proposed method. In addition, by comparing the prediction results with and without coupling between axial tension and VIV responses, it is found that this coupling effect is of importance to VIV prediction and can improve VIV prediction accuracy, especially under the case of high flow velocity and high vibration mode.

In this paper, a time-domain hydroelastic method for very large floating structures (VLFS′) in inhomogeneous waves is developed based on Cummins' equation. By discretizing the continuous VLFS into rigid modules connected by elastic beam elements, the inhomogeneous wave effect can be considered by adopting different wave spectra over different regions of the VLFS. In this method, the frequency-domain hydrodynamic coefficients, considering the hydrodynamic interactions between each floating module, are transformed into the time-domain hydroelastic model using Cummins' equation. Moreover, the time-domain wave excitation forces on the modules in different regions are solved using different wave spectra. The hydroelastic responses of a freely floating structure in inhomogeneous regular and irregular waves are investigated. The results show that the inhomogeneity of waves has a significant effect on the bending moments, shear forces and torsional moments of the structure, especially for a wave direction of 90°, in which larger forces may be induced compared with the homogeneous waves.

A method to identify vortex-induced forces and coefficients from measured strains of a Steel Catenary Riser (SCR) undergoing vessel motion-induced Vortex-induced Vibration (VIV) is proposed. Euler–Bernoulli beam vibration equations with time-varying tension is adopted to describe the out-of-plane VIV responses. Vortex-induced forces are reconstructed via inverse analysis method, and the Forgetting Factor Least Squares (FF-LS) method is employed to identify time-varying vortex-induced force coefficients, including excitation coefficients and added mass coefficients. The method is verified via a finite element analysis procedure in commercial software Orcaflex. The time-varying excitation coefficients and added mass coefficients of an SCR undergoing vessel motion-induced VIV are investigated. Results show that vessel motion-induced VIV is excited at the middle or lower part of the SCR and in the acceleration period of in-plane velocity, where most of the excitation coefficients are positive, while during the deceleration period, the excitation coefficients becomes too small to excite VIVs. Parameter γ [1] has strong correlation with excitation coefficients. In addition, time-varying tensions contribute significantly to the variations of added mass coefficients under the condition that the ratio of dynamic top tension to pretension exceeds the range of 0.7–1.3. Moreover, chaotic behaviors are observed in vortex-induced force coefficients and are more evident with the increase of vessel motion velocity. This behavior may attribute to the randomness existing in in-plane velocity and its coupling with out-of-plane vibrations.

A large-scale model test of a free-hanging water intake riser (WIR) is performed in an ocean basin to investigate the riser responses under vessel motion. Top end of the WIR is forced to oscillate at given vessel motion trajectories. Fiber Brag Grating (FBG) strain sensors are used to measure the WIR dynamic responses. Experimental results firstly confirms that the free-hanging WIR would experience out-of-plane vortex-induced vibrations (VIVs) under pure vessel motion even for the case with a KC number as low as 5. Meanwhile, comparison between numerical results and experimental measurements suggests a significant drag amplification by out-of-plane vessel motion-induced VIV. What’s more, further study on WIR response frequencies and cross section trajectories reveals a strong correlation between vessel motion-induced VIV and local KC number distribution, owing to the small KC number effect. The presented work provides useful references for gaining a better understanding on VIV induced by vessel motion, and for the development of future prediction models.

This paper presents theoretical and numerical study on bending properties of unbonded flexible risers. To capture nonlinearities in layer's sliding, the stress component due to slip-stick behavior is considered and energy conservation principle considering sliding-caused heat consumption is employed in the analytical model. Besides, a finite element model estimating mechanics of unbonded flexible risers' bending is proposed. In the finite element model, couplings between bending moment–curvature and axial stress as well as contact interaction among layers and tendons have been considered. The theoretical and numerical results were validated against the corresponding experimental data in literature and mutually compared in analyzing nonlinear bending behavior of flexible risers. Moreover, the impacts of axisymmetric loads on riser's bending behavior have been further investigated.

Vortex-induced vibration (VIV) of a flexible cylinder in oscillatory flow was experimentally investigated in an ocean basin. An intermittent VIV was confirmed to have occurred during the tests. The fatigue damage caused by VIV was calculated based on rainflow counting and a standard S–N curve. There are 3 main observations for fatigue damage from VIV in oscillatory flow: 1) the damage varied significantly with the KC number, which is a unique feature for VIV in oscillatory flow. 2) Fatigue damage at small KC number cases was found to be larger compared to those at large KC numbers owing to the fact that number of vortex shedding cycles per half of the motion cycle is low, and damping within half of the motion cycle will hence become low. The fact that vortices from the previous cycle still are active during the next may also contribute to the large response at small KC numbers. 3) ‘Amplitude modulation’ and ‘mode transition’, two specific features for VIV in oscillatory flow, were found to have a strong influence on fatigue. Fatigue damage has also been calculated by an empirical VIV prediction model assuming that all cases have steady flow at an equivalent velocity. Finally, a simplified method for calculating fatigue damage from VIV in oscillatory flow based on steady flow conditions is proposed. A modification factor diagram is presented, but the scope of the present study is too limited to provide a good basis for a general model for this factor. A general model for how to apply results from constant current analysis to predict fatigue in oscillatory flow will therefore need further research.

Many significant engineering challenges have emerged as the petroleum industry has moved their field development and production activities into increasingly deeper water depths. The design of deepwater marine risers presents the combined challenges to minimize top tensioning requirements, mitigate any flow-induced vibrations, and if possible to increase the expected fatigue life of these slender structural members. As part of the design process to achieve these goals external buoyancy modules and strakes have been employed. To gain insight into the complex multi-mode response behavior a recent experimental study was performed and the analysis of selected data sets is presented. In the experiments a horizontal cylinder with a length to diameter ratio of 263 was fitted with a variety of strake and buoyancy element configurations. The models were towed at uniform speeds ranging from 0.4 to 2.0 m/s and fiber optic strain gages were used to measure both in-line and cross-flow strain response. The resulting time series information was processed utilizing the method of time domain decomposition formulated for strain data input and the introduction of modal assurance criterion to resolve the modal strain information that included frequency, mode shape, and critical damping ratio information. The pre-tensioned cylinder without appendages was used as a base case and the results were basically consistent with expectations. In the case of 0.8 m/s low-tension test, multiple closely spaced non-overlapping peaks were observed in both in-line and cross-flow directions and were identified as being of the same mode with mode shapes distorted away from purely sinusoidal behavior. The test data for the 100% coverage by helical stakes demonstrated the effectiveness of that suppression device over the range of current velocities investigated. The most interesting case was that of a staggered combination of helical strakes and buoyancy element whose total for each type of coverage was equal. This effective asymmetric VIV suppression approach is presented and discussed in detail.

A large-scale model test of a truncated steel catenary riser (SCR) was performed in an ocean basin to investigate the vortex-induced vibration (VIV) and its fatigue damage under pure top vessel motion. The top end of the test model was forced to oscillate at given vessel motion trajectories. Fiber Bragg grating (FBG) strain sensors were used to measure both in-plane and out-of-plane responses. Four different factors have been discussed to understand the VIV responses and fatigue damage results: instantaneous shedding frequency, touch down point (TDP) variation, tension variation and traveling waves. Out-of-plane VIV associated with strong time-varying features was confirmed to have occurred under pure vessel motion. Both KC number and maximum shedding frequency were investigated and indicated that the middle part of the truncated model riser was the ‘power-in’ region for out-of-plane VIV. Meanwhile, fatigue damage caused by out-of-plane VIV was found to be strongly dependent on both top motion amplitude and period. The probability distribution of the maximum damage exhibits 3 critical locations in the test model: TDP, upper sag-bend and top of the SCR. Strong traveling waves, TDP variation and end wave reflection have been proven to cause the maximum damage locations to shift from the ‘power-in’ region to these three positions. Finally, a maximum fatigue damage diagram with top motion amplitude, period and maximum shedding frequency was constructed.

In this paper, an investigation of the nonlinear hydroelastic response of a deep-water gravity aquaculture fish cage in irregular waves is described. Beam elements, truss elements, and nonlinear springs were used to simulate the motion and deformation of the floating collar, the net, and the mooring lines, respectively, in a finite element model, where large-deformation geometric nonlinearities were also taken into account. Irregular waves were simulated by choosing a suitable wave spectrum, and the nonlinearities of the wave loads were also considered. The instantaneous buoyancy forces on the floating collar were considered by use of the “distributed beam method.” The dynamic displacement response of the collar in irregular waves, the modal contribution from each mode shape, the reduction of the fish cage volume, and the mooring-line forces were studied.

In this paper the hydrodynamic characteristics of a floating cylinder are investigated via forced oscillation experiments in towing tank. The effects of Keulegan–Carpenter number, Reynolds number, reduced velocity and overtopping on hydrodynamics of the floating cylinder in oscillatory and steady flow are studied. The results show a considerably difference of the hydrodynamic characters between the floating and the fully immerged cylinders due to the influences of free surface. The growth of the reduced velocity, a proven notable effect on hydrodynamics, will lead to the increase of added mass coefficient and the decrease of drag coefficient. Meanwhile the overtopping, a particular phenomenon for the floating cylinder, render the added mass coefficients reach up to 3.6 while for the drag coefficient small influences were made.

The moving loads induced hydroelastic responses of a ribbon floating bridge composed of several nonlinearly connected modules are studied from both experimental and numerical aspects in this paper. The 1:10 model tests were conducted in the ocean basin, where the static responses by static loads and dynamic vertical displacements of the floating bridge induced by moving loads were measured. The corresponding responses were also simulated numerically based on finite element method, and are finally compared with the experimental results. The results from the static cases validated the simulations of the connectors' properties. The dynamic responses show the main characteristics of the ribbon bridge under moving loads. The results show that the nonlinearity of the connectors has a great influence on the dynamic response of the floating bridge especially for the upward dynamic responses.

In this paper, the prediction of the hydroelastic response of the floating bridge and the fatigue behavior of the connectors is presented. And based on the hydroelastic response analysis of the ribbon bridge, the dynamic alternating load of the connector can be obtained, in that the fatigue behavior analysis of the connector simulated by the solid elements can be conducted by employing the local stress–strain approach. It is revealed that the sequence of the dynamic loads acting on the connectors, the value of various fatigue parameters and the ultimate tensile strength should be sufficiently considered, especially the passing speed of a moving load, so that it can significantly reduce the fatigue damage of the connectors.