Coupled Cross-Flow/in-Line Vortex-Induced Vibration Responses of a Catenary-Type Riser Subjected to Uniform Flows

A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration (VIV) of a catenary-type riser (CTR) in the in-line (IL) and cross-flow (CF) directions. By using the vector form intrinsic finite element method, the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law. The Van der Pol oscillator was used to simulate the effect of vortex shedding. The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm. The numerical model was verified with the published results. The VIV characteristics of the CTR subjected to uniform flows, including displacement, frequency, standing wave, traveling wave, motion trajectory, and energy transfer, were studied comprehensively. The numerical results revealed that the multimode property occurs in the CF- and IL-direction VIV responses of the CTR. An increase in the flow velocity has slight effects on the maximum VIV displacement. Due to structural nonlinearity, the double-frequency relationship in the CF and IL directions is rarely captured. Therefore, the vibration trajectories display the shape of an inclined elliptical orbit. Moreover, the negative energy region is inconspicuous under the excitation of the uniform flow.