When seawater streams around risers, it causes vortex-induced vibrations (VIV), which occur in two forms: in-line (IL) and cross-flow (CF). Accurate prediction of coupled IL and CF VIV behaviors are essential for designing risers. The use of the van der Pol nonlinear wake oscillator model has proven effective in capturing the complex interactions between the riser dynamics and the variable hydrodynamic forces caused by vortex shedding in varying flow conditions. This work analyzes the IL and CF VIV responses by risers in a linear shear flow, employing a double diffusive van der Pol oscillator and the generalized integral transform technique(GITT). Represented as an Euler-Bernoulli beam, the riser accounts for spatial variations in tension as well as IL and CF directions. Hydrodynamic forces impacting the riser are represented by two wake oscillators. The coupled system of nonlinear partial differential equation set further transformed into a nonlinear ordinary differential equation system, which is truncated at a finite order to allow numerical solutions using well-established algorithms. This work investigates the VIV response of the riser in both CF and IL directions, as well as the effects of different top tensions and types of currents on the three-dimensional VIV displacement of the riser. The results indicate that the vibration mode of the riser is influenced by both CF and IL directions, and the impact of the IL direction cannot be ignored.
Vortex-induced vibration(VIV), as an important form of interaction between fluid and structure, involves periodic oscillations that not only affect the structural fatigue life but can also lead to structural damage through resonance-induced large-amplitude oscillations. Nonlinear wake oscillators have found extensive application in simulating the interaction between the oscillating riser and the time-dependent hydrodynamic forces, in both uniform and shear flow conditions (Facchinetti et al., 2002, 2004). Gu et al. (2012) used a wake oscillator model along with the generalized integral transform technique (GITT) to predict the VIV responses in a vertical riser. Gao et al. (2022) investigated the VIV of a marine riser under varying tension and three different types of shear flow, using a wake oscillator model and the finite difference method. With the use of wake oscillator models, there has been a growing focus on understanding the influence of the bidirectionally coupled VIV response of risers. Gao et al. (2020) used wake oscillators and finite element methods to predict the bidirectional VIV responses of a riser in the linear shear flow, considering changes in added mass.
