PDEM-based uncertainty quantification framework of the coupled cross-flow and inline vortex-induced vibrations for flexible cylinders considering elastic boundaries

Traditional analytical and prediction tools for vortex-induced vibration (VIV) of flexible cylinders usually ignore the random nature and treat the boundary constraint as ideally hinged or fixed for simplicity, which may yield results that differ from reality. In this paper, the distributed Van-der-pol oscillators coupled with the EulerBernoulli beam equations are employed to model the cross-flow (CF) and inline (IL) VIVs of flexible cylinders, and the elastic boundary is considered by introducing an additional rotation constraint on the hinge support. Then, a nonlinear stochastic VIV analysis model is established by systematically considering the randomness of the structural properties, hydrodynamic variables, and wake oscillator coefficients. On this basis, an effective VIV uncertainty quantification (UQ) framework is proposed based on the probability density evolution method (PDEM). Finally, two examples are used to demonstrate the implementation of the proposed framework. The results show that for the bending-dominated cylinder, the probability density function (PDF) evolution of the response in both directions exhibits a unimodal distribution, and the deviation of responses decreases with increased elastic constraints. However, the response PDFs of the tension-dominated cylinder present bimodal and unimodal distributions in the CF and IL directions, respectively, and responses are insensitive to changes in boundary conditions.