This paper is first of the two papers dealing with the nonlinear modelling and investigation of coupled cross-flow and in-line vortex-induced vibrations (VIVs) of flexible cylindrical structures. As a continuation of the previous work (Qu and Metrikine in Ocean Eng 196:106732, 2020) where a new single wake oscillator model was proposed and studied for VIVs of rigid cylinders, the present paper focuses on applying it to flexible cylinders. In this paper, the structure is modelled as an extensible Euler–Bernoulli beam and its 3D nonlinear coupling motion is described in the absolute coordinate system. The single van der Pol wake oscillator model with nonlinear coupling to the in-line motion of the structure, in addition to the classic linear cross-flow motion coupling, is uniformly distributed along the structure to model the hydrodynamic force acting on it. The finite element method has been applied to solve the dynamics of the coupled system, and the experiments of the VIV of a top-tensioned straight riser subjected to a step flow have been taken for the validation of the model. The model has been shown to be able to capture most features of VIVs of flexible cylinders, and a good agreement between the simulation results and the experimental measurements has been observed with regard to the amplitude, frequency and excited mode of both cross-flow and in-line vibrations, as well as the mean in-line deflection due to the amplified in-line force. While it is conventionally expected that the VIV of a flexible cylinder subjected to a uniform flow is dominated by a single frequency, a multi-frequency response is observed in the simulation results over the range of flow velocities through which the transition of the dominant mode of vibration occurs.

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An experimental investigation on the coupled dynamics of an offshore tunnel-rig system from the element launching to its near-seabed immersion in irregular waves is conducted, where the motions of tunnel/rigs and the tensile forces of the suspension lines are evaluated in a synchronous manner for a wide range of irregular waves. The effect of immersion depth on the coupled dynamics of the tunnel-rigs system, especially the relationship between the relative motion and suspension line tensions are experimentally examined. The system coupling mechanism is further addressed using the modal analysis and response spectra analysis. The results show that the natural frequencies of the coupled system are primarily affected by the varying immersion depth. The increasing immersion depth leads to a larger in-phase roll period of the system and a greater roll resonance amplitude. For a given immersion depth, a strong dependence of the suspension line tensions upon the relative motions is established.

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The authors regret that there are a few typological errors in Eqs. (9) and (13) and (15)–(17). For Eqs. (9), (13) and (17), the signs of the first terms are wrong and they should be corrected as follows: [Formula presented] [Formula presented] [Formula presented] A symbol L is missing on the right hand sides of Eqs. (15) and (16) and they should be corrected as follows: [Formula presented] [Formula presented] The authors would like to apologise for any inconvenience caused.

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In this study a new wake oscillator model is proposed to describe the coupled cross-flow and in-line vortex-induced vibrations of an elastically supported rigid cylinder. Different from many other studies where two wake oscillators have been applied, the current model uses only one wake oscillator coupled to both cross-flow and in-line motions. The new model is based on the van der Pol oscillator with the classic acceleration coupling between the wake and cross-flow motion, while the in-line motion is coupled with the wake variable in a nonlinear manner. The predictions of this new model are compared with the existing experimental data and shown to be in good agreement. In addition to the conventional lock-in range that corresponds to reduced velocities between 5 and 8, another lock-in is predicted around reduced velocity of 2.5 due to the in-line vibration. Most importantly, the new model is proved to be able to predict the appearance of the ‘super-upper’ branch at small mass ratios without changing the tuning parameters. The limitations of the model associated with unrealistic predictions of free vibrations with very small mass ratios and those of forced in-line vibrations at high frequencies are also discussed along with a possible remedy.@en

To illustrate the influence of the in-line coupling on the prediction of vortex-induced vibration (VIV), the simulation results of the coupled cross-flow and in-line VIVs of flexible cylinders- obtained with three different wake oscillator models with and without the in-line coupling- are compared and studied in this paper. Both the cases of uniform and linearly sheared flow are analysed and the simulation results of the three models are compared with each other from the viewpoints of response pattern, fluid force, energy transfer and fatigue damage. The differences between the simulation results from the three models highlight the importance of the in-line coupling on the prediction of coupled cross-flow and in-line VIVs of flexible cylindrical structures.

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In this paper, a new wake oscillator model with nonlinear coupling is proposed for the modelling of vortex-induced vibration. The purpose is to develop a model that is capable of reproducing both free and forced vibration experiments. To achieve this goal, an existing van der Pol wake oscillator model is first reviewed. The limitations of the model are discussed and the influence of different drag force models on the dynamic characteristics of the fluctuating lift force that matches the forced vibration experiments are studied. Based on this model, nonlinear coupling terms are introduced to improve its predictive capabilities. The tuning of this improved model to the forced vibration shows a good agreement with experiments in terms of the added damping. However, the model failed to capture the negative added mass at high reduced velocities. As a result, the new model underpredicts both the range and frequency of lock-in in free vibration tests. To eliminate this discrepancy, the model is further enhanced by introducing frequency dependent nonlinear couplings, which are achieved in the time domain by means of convolution integrals. A single set of frequency dependent, complex-valued functions – which are the Laplace transforms of corresponding convolution kernels – that reproduce the forced vibration experiments is determined over a limited range of frequencies. However, no analytical extension of these functions to the infinite frequency domain was found such that the causality principle and the energy conservation would be satisfied. The latter is a major challenge for all existing wake oscillator models that aim at reproducing the forced vibration experiments.

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Vortex-induced vibration (VIV) is awell-known phenomenon for civil and offshore structures. Currently, the prediction of this type of vibration in practice currently mainly relies on the force-decomposition method. However, the limitations of this method have restricted the applicability of the method, and alternative models are therefore needed to meet increasing demands for the more accurate prediction of VIV under more complicated conditions. The wake oscillator model overcomes the main limitations of the force-decomposition method to some extent, and it is one of the promising models that has gained popularity in recent years. Although the concept of the wake oscillator was first proposed over half a century ago and has been developed much since then, the existing wake oscillator models still have some limitations, which have restricted their applications. The main objective of this study is to improve the wake oscillator model for better modelling of the VIV of cylindrical structures, and efforts are made in this thesis to (a) reproduce the free and forced vibration experiments by introducing nonlinear coupling, and (b) develop a single wake oscillator equation that is coupled to both cross-flow and in-line motions for the prediction of coupled cross-flow and in-line VIV...@en

This work reports on experiments that were performed with a freely vibrating cylinder exposed to currents and placed near a plane boundary parallel to the cylinder axis. It is observed that the proximity of the boundary affects the vertical response of the cylinder in two ways: (i) for gaps between 0.75 and 2 diameters (D), the amplitude of oscillation is reduced; (ii) for gaps smaller than 0.75D, the cylinder impacts the boundary, resulting in an increase of amplitudes and frequencies of oscillations as the flow is accelerated. The in-line force acting on the cylinder is also examined, and the dependency of its harmonic components on the flow velocity and distance to the boundary is evaluated. Besides the typical amplification of the mean component inside the lock-in region, it is also observed that as the cylinder is placed closer to the boundary, the harmonic component with the frequency of the vertical oscillations increases, while the component with twice that frequency decreases in similar amount.

Based on the experimental observations, an existing wake-oscillator model for vortex-induced vibrations is enhanced in order to account for the effect of the boundary. The proposed model introduces an effective damper that is activated when the cylinder reaches a certain distance from the boundary, and a damper/spring set representing the rigidity of the boundary and the dissipation of energy due to impact.
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In this paper a new wake oscillator model with nonlinear coupling term is proposed to model the vortex-induced vibration of an elastically supported rigid cylinder constrained to vibrate in the cross-flow direction. The superiority of this new model lies in its ability to satisfy at the same time both free and forced vibration experiments. The new wake oscillator model is based on an existing van der Pol wake oscillator model and nonlinear coupling terms are added to improve its performance in the modelling of forced vibration. The tuning of this new model to the forced vibration shows good agreement with experiments in terms of the added damping but failed to capture the negative added mass at high reduced velocities. To eliminate this discrepancy the model is further enhanced by relaxing the assumption of constant potential added mass. Using the parameters obtained from the forced vibration experiments, the free vibration simulation is conducted and results are compared with the experiments. Comparison indicates good agreement between simulation and experiments, and the main features of VIV are captured.@en