Nonlinear Response of Marine Riser with Large Displacement Excited by Top-End Vessel Motion using Penalty Method

A marine riser operated in a deep-water field could be substantially affected by large amounts of movement of the floating platform, which is more complicated and very challenging to analyze. This paper presents a mathematical model involving nonlinear dynamic response analysis of a marine riser caused by sways and heave motions at the top end, which are treated as the constraint conditions. The nonlinear equation of motion, arising from the nonlinearity of the ocean current and wave loadings, is derived and written in general matrix form using the finite element method. The excitation caused by platform movement is imposed on the riser system through the time-dependent constrained condition using the penalty method. The advantages of this method are that it is easily implemented on the nonlinear equation of motion and it requires no additional unknown variable, and thus consumes less computational time. By this method, the stiffness matrix and the force vector of the system are then modified, enforcing top-end vessel motion. The dynamic responses are evaluated by using numerical time integration based on Newmark's method with direct iteration. The effects of the oscillation frequency of top-end vessel sway and heave motions on the nonlinear dynamic characteristics of the riser are investigated. The numerical results reveal that the riser responses to the top-end vessel excitation behave like a periodic motion, which is conformable to the characteristics of vessel movements. The increase in the oscillation frequency of the top-end vessel increases the maximum displacement amplitude for both the horizontal and vertical directions. The directional motion of the vessel also significantly influences the response amplitude of the riser.