Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part I: model description and validation

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.