This paper presents a variational model of a deepwater marine riser transporting fluid capable of analyzing large amplitude motions. The riser model is formulated based on the virtual work-energy principle. The geometric nonlinearity is considered, which accounts for axial stretching and the deformed curvature of the riser. The finite element method is used to solve the numerical solution. The nonlinear stiffness matrices up to second order of riser displacements are kept in the equation of motion. The hydrodynamic force written in term of squared riser velocity also yields the nonlinear damping matrix. The inertial force induced by an unsteady flow of transported fluid is taken into consideration. Performing the Newmark time integration incorporated direct iteration on the equation of motion provides the nonlinear vibration response. For the parametric studies, the effect of forcing frequencies of hydrodynamic wave and internal pulsatile flow on the dynamic responses are highlighted. The special attentions are paid to the effect of nonlinear geometry on vibration amplitude of the riser.
The marine riser is a slender pipe used in offshore petroleum drilling and production processes for conveying crude oil from a seabed up to a production platform (Sparks, 2007). In addition to its self-weight, for deepwater, the riser also receives high hydrostatic pressure, and harsh hydrodynamic current and wave loadings. These environmental loadings exerted on marine riser system will lead to its complex analyses.
For deepwater operation, the analysis of riser begins with finding its static configuration. From literature reviews, many researchers have developed the alternative model formulations and the solution methods for capturing the large displacement analysis of the riser (Chucheepsakul et al., 2003; Chai and Varyani, 2006; Athisakul et al., 2012; Athisakul et al., 2014; Gay Neto et al., 2014). Beyond the static analysis, it also requires the nonlinear dynamic analysis to concern the nonlinear environmental forces, at least for the hydrodynamic ocean force, which are nonlinear in nature. Moreover, different types of environmental loadings are combined together to predict a realistic dynamic response of riser, for example, the response caused by vortex induced vibration, internal unsteady flow, and top end excitation, which can be found in Bar-Avi (2000), Monprapussorn et al., (2007), Srinil et al. (2011), Chen et al. (2015), and Lei et al. (2015). These previous works presented the vibration response of the marine riser excited by combined environmental loads, which was capable of reasonably describing the nonlinear dynamic characteristics. However, their results were based on the assumption of small amplitude dynamic displacement.